diff --git a/libcxx/docs/Status/RangesAlgorithms.csv b/libcxx/docs/Status/RangesAlgorithms.csv
--- a/libcxx/docs/Status/RangesAlgorithms.csv
+++ b/libcxx/docs/Status/RangesAlgorithms.csv
@@ -76,7 +76,7 @@
 Permutation,sort,Konstantin Varlamov,`D127557 <https://llvm.org/D127557>`_,✅
 Permutation,stable_sort,Konstantin Varlamov,n/a,In progress
 Permutation,partial_sort,Konstantin Varlamov,n/a,In progress
-Permutation,nth_element,Not assigned,n/a,Not started
+Permutation,nth_element,Konstantin Varlamov,`TODO <https://llvm.org/TODO>`_,Not started
 Permutation,inplace_merge,Not assigned,n/a,Not started
 Permutation,make_heap,Not assigned,n/a,Not started
 Permutation,push_heap,Not assigned,n/a,Not started
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -100,6 +100,7 @@
   __algorithm/ranges_minmax_element.h
   __algorithm/ranges_mismatch.h
   __algorithm/ranges_none_of.h
+  __algorithm/ranges_nth_element.h
   __algorithm/ranges_replace.h
   __algorithm/ranges_replace_if.h
   __algorithm/ranges_reverse.h
diff --git a/libcxx/include/__algorithm/nth_element.h b/libcxx/include/__algorithm/nth_element.h
--- a/libcxx/include/__algorithm/nth_element.h
+++ b/libcxx/include/__algorithm/nth_element.h
@@ -15,6 +15,7 @@
 #include <__config>
 #include <__debug>
 #include <__iterator/iterator_traits.h>
+#include <__utility/move.h>
 #include <__utility/swap.h>
 
 #if defined(_LIBCPP_DEBUG_RANDOMIZE_UNSPECIFIED_STABILITY)
@@ -28,220 +29,228 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template<class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 bool
-__nth_element_find_guard(_RandomAccessIterator& __i, _RandomAccessIterator& __j,
-                         _RandomAccessIterator __m, _Compare __comp)
-{
-    // manually guard downward moving __j against __i
-    while (true) {
-        if (__i == --__j) {
-            return false;
-        }
-        if (__comp(*__j, *__m)) {
-            return true;  // found guard for downward moving __j, now use unguarded partition
-        }
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool __nth_element_find_guard(_RandomAccessIterator& __i, _RandomAccessIterator& __j,
+                              _RandomAccessIterator __m, _Compare __comp) {
+  // manually guard downward moving __j against __i
+  while (true) {
+    if (__i == --__j) {
+      return false;
     }
+    if (__comp(*__j, *__m)) {
+      return true;  // found guard for downward moving __j, now use unguarded partition
+    }
+  }
 }
 
 template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 void
-__nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last, _Compare __comp)
-{
-    // _Compare is known to be a reference type
-    typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
-    const difference_type __limit = 7;
-    while (true)
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last,
+                   _Compare __comp) {
+  // _Compare is known to be a reference type
+  using difference_type = typename iterator_traits<_RandomAccessIterator>::difference_type;
+  const difference_type __limit = 7;
+
+  while (true) {
+    if (__nth == __last)
+      return;
+
+    difference_type __len = __last - __first;
+    switch (__len)
     {
-        if (__nth == __last)
-            return;
-        difference_type __len = __last - __first;
-        switch (__len)
+      case 0:
+      case 1:
+        return;
+      case 2:
+        if (__comp(*--__last, *__first))
+          swap(*__first, *__last);
+        return;
+      case 3:
         {
-        case 0:
-        case 1:
-            return;
-        case 2:
-            if (__comp(*--__last, *__first))
-                swap(*__first, *__last);
-            return;
-        case 3:
-            {
-            _RandomAccessIterator __m = __first;
-            _VSTD::__sort3<_Compare>(__first, ++__m, --__last, __comp);
-            return;
-            }
-        }
-        if (__len <= __limit)
-        {
-            _VSTD::__selection_sort<_Compare>(__first, __last, __comp);
-            return;
+          _RandomAccessIterator __m = __first;
+          std::__sort3<_Compare>(__first, ++__m, --__last, __comp);
+          return;
         }
-        // __len > __limit >= 3
-        _RandomAccessIterator __m = __first + __len/2;
-        _RandomAccessIterator __lm1 = __last;
-        unsigned __n_swaps = _VSTD::__sort3<_Compare>(__first, __m, --__lm1, __comp);
-        // *__m is median
-        // partition [__first, __m) < *__m and *__m <= [__m, __last)
-        // (this inhibits tossing elements equivalent to __m around unnecessarily)
-        _RandomAccessIterator __i = __first;
-        _RandomAccessIterator __j = __lm1;
-        // j points beyond range to be tested, *__lm1 is known to be <= *__m
-        // The search going up is known to be guarded but the search coming down isn't.
-        // Prime the downward search with a guard.
-        if (!__comp(*__i, *__m))  // if *__first == *__m
-        {
-            // *__first == *__m, *__first doesn't go in first part
-            if (_VSTD::__nth_element_find_guard<_Compare>(__i, __j, __m, __comp)) {
-                swap(*__i, *__j);
-                ++__n_swaps;
-            } else {
-                // *__first == *__m, *__m <= all other elements
-                // Partition instead into [__first, __i) == *__first and *__first < [__i, __last)
-                ++__i;  // __first + 1
-                __j = __last;
-                if (!__comp(*__first, *--__j)) {  // we need a guard if *__first == *(__last-1)
-                    while (true) {
-                        if (__i == __j) {
-                            return;  // [__first, __last) all equivalent elements
-                        } else if (__comp(*__first, *__i)) {
-                            swap(*__i, *__j);
-                            ++__n_swaps;
-                            ++__i;
-                            break;
-                        }
-                        ++__i;
-                    }
-                }
-                // [__first, __i) == *__first and *__first < [__j, __last) and __j == __last - 1
-                if (__i == __j) {
-                    return;
-                }
-                while (true) {
-                    while (!__comp(*__first, *__i))
-                        ++__i;
-                    while (__comp(*__first, *--__j))
-                        ;
-                    if (__i >= __j)
-                        break;
-                    swap(*__i, *__j);
-                    ++__n_swaps;
-                    ++__i;
-                }
-                // [__first, __i) == *__first and *__first < [__i, __last)
-                // The first part is sorted,
-                if (__nth < __i) {
-                    return;
-                }
-                // __nth_element the second part
-                // _VSTD::__nth_element<_Compare>(__i, __nth, __last, __comp);
-                __first = __i;
-                continue;
+    }
+
+    if (__len <= __limit) {
+      std::__selection_sort<_Compare>(__first, __last, __comp);
+      return;
+    }
+
+    // __len > __limit >= 3
+    _RandomAccessIterator __m = __first + __len/2;
+    _RandomAccessIterator __lm1 = __last;
+    unsigned __n_swaps = std::__sort3<_Compare>(__first, __m, --__lm1, __comp);
+    // *__m is median
+    // partition [__first, __m) < *__m and *__m <= [__m, __last)
+    // (this inhibits tossing elements equivalent to __m around unnecessarily)
+    _RandomAccessIterator __i = __first;
+    _RandomAccessIterator __j = __lm1;
+    // j points beyond range to be tested, *__lm1 is known to be <= *__m
+    // The search going up is known to be guarded but the search coming down isn't.
+    // Prime the downward search with a guard.
+    if (!__comp(*__i, *__m))  // if *__first == *__m
+    {
+      // *__first == *__m, *__first doesn't go in first part
+      if (std::__nth_element_find_guard<_Compare>(__i, __j, __m, __comp)) {
+        swap(*__i, *__j);
+        ++__n_swaps;
+      } else {
+        // *__first == *__m, *__m <= all other elements
+        // Partition instead into [__first, __i) == *__first and *__first < [__i, __last)
+        ++__i;  // __first + 1
+        __j = __last;
+        if (!__comp(*__first, *--__j)) {  // we need a guard if *__first == *(__last-1)
+          while (true) {
+            if (__i == __j) {
+              return;  // [__first, __last) all equivalent elements
+            } else if (__comp(*__first, *__i)) {
+              swap(*__i, *__j);
+              ++__n_swaps;
+              ++__i;
+              break;
             }
+            ++__i;
+          }
         }
-        ++__i;
-        // j points beyond range to be tested, *__lm1 is known to be <= *__m
-        // if not yet partitioned...
-        if (__i < __j)
-        {
-            // known that *(__i - 1) < *__m
-            while (true)
-            {
-                // __m still guards upward moving __i
-                while (__comp(*__i, *__m))
-                    ++__i;
-                // It is now known that a guard exists for downward moving __j
-                while (!__comp(*--__j, *__m))
-                    ;
-                if (__i >= __j)
-                    break;
-                swap(*__i, *__j);
-                ++__n_swaps;
-                // It is known that __m != __j
-                // If __m just moved, follow it
-                if (__m == __i)
-                    __m = __j;
-                ++__i;
-            }
+
+        // [__first, __i) == *__first and *__first < [__j, __last) and __j == __last - 1
+        if (__i == __j) {
+          return;
         }
-        // [__first, __i) < *__m and *__m <= [__i, __last)
-        if (__i != __m && __comp(*__m, *__i))
-        {
-            swap(*__i, *__m);
-            ++__n_swaps;
+        while (true) {
+          while (!__comp(*__first, *__i))
+            ++__i;
+          while (__comp(*__first, *--__j))
+            ;
+          if (__i >= __j)
+            break;
+          swap(*__i, *__j);
+          ++__n_swaps;
+          ++__i;
         }
-        // [__first, __i) < *__i and *__i <= [__i+1, __last)
-        if (__nth == __i)
-            return;
-        if (__n_swaps == 0)
-        {
-            // We were given a perfectly partitioned sequence.  Coincidence?
-            if (__nth < __i)
-            {
-                // Check for [__first, __i) already sorted
-                __j = __m = __first;
-                while (true) {
-                    if (++__j == __i) {
-                        // [__first, __i) sorted
-                        return;
-                    }
-                    if (__comp(*__j, *__m)) {
-                        // not yet sorted, so sort
-                        break;
-                    }
-                    __m = __j;
-                }
-            }
-            else
-            {
-                // Check for [__i, __last) already sorted
-                __j = __m = __i;
-                while (true) {
-                    if (++__j == __last) {
-                        // [__i, __last) sorted
-                        return;
-                    }
-                    if (__comp(*__j, *__m)) {
-                        // not yet sorted, so sort
-                        break;
-                    }
-                    __m = __j;
-                }
-            }
+
+        // [__first, __i) == *__first and *__first < [__i, __last)
+        // The first part is sorted,
+        if (__nth < __i) {
+          return;
         }
-        // __nth_element on range containing __nth
-        if (__nth < __i)
-        {
-            // _VSTD::__nth_element<_Compare>(__first, __nth, __i, __comp);
-            __last = __i;
+
+        // __nth_element the second part
+        // std::__nth_element<_Compare>(__i, __nth, __last, __comp);
+        __first = __i;
+        continue;
+      }
+    }
+
+    ++__i;
+    // j points beyond range to be tested, *__lm1 is known to be <= *__m
+    // if not yet partitioned...
+    if (__i < __j) {
+      // known that *(__i - 1) < *__m
+      while (true) {
+        // __m still guards upward moving __i
+        while (__comp(*__i, *__m))
+          ++__i;
+
+        // It is now known that a guard exists for downward moving __j
+        while (!__comp(*--__j, *__m))
+          ;
+        if (__i >= __j)
+          break;
+        swap(*__i, *__j);
+        ++__n_swaps;
+
+        // It is known that __m != __j
+        // If __m just moved, follow it
+        if (__m == __i)
+          __m = __j;
+        ++__i;
+      }
+    }
+
+    // [__first, __i) < *__m and *__m <= [__i, __last)
+    if (__i != __m && __comp(*__m, *__i)) {
+      swap(*__i, *__m);
+      ++__n_swaps;
+    }
+
+    // [__first, __i) < *__i and *__i <= [__i+1, __last)
+    if (__nth == __i)
+      return;
+    if (__n_swaps == 0) {
+      // We were given a perfectly partitioned sequence.  Coincidence?
+      if (__nth < __i) {
+        // Check for [__first, __i) already sorted
+        __j = __m = __first;
+        while (true) {
+          if (++__j == __i) {
+            // [__first, __i) sorted
+            return;
+          }
+          if (__comp(*__j, *__m)) {
+            // not yet sorted, so sort
+            break;
+          }
+          __m = __j;
         }
-        else
-        {
-            // _VSTD::__nth_element<_Compare>(__i+1, __nth, __last, __comp);
-            __first = ++__i;
+
+      } else {
+        // Check for [__i, __last) already sorted
+        __j = __m = __i;
+        while (true) {
+          if (++__j == __last) {
+            // [__i, __last) sorted
+            return;
+          }
+          if (__comp(*__j, *__m)) {
+            // not yet sorted, so sort
+            break;
+          }
+          __m = __j;
         }
+      }
+    }
+
+    // __nth_element on range containing __nth
+    if (__nth < __i) {
+      // std::__nth_element<_Compare>(__first, __nth, __i, __comp);
+      __last = __i;
+    } else {
+      // std::__nth_element<_Compare>(__i+1, __nth, __last, __comp);
+      __first = ++__i;
     }
+  }
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last, _Compare __comp)
-{
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void __nth_element_impl(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last,
+                        _Compare& __comp) {
   _LIBCPP_DEBUG_RANDOMIZE_RANGE(__first, __last);
-  typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-  _VSTD::__nth_element<_Comp_ref>(__first, __nth, __last, __comp);
+
+  using _Comp_ref = typename __comp_ref_type<_Compare>::type;
+  std::__nth_element<_Comp_ref>(__first, __nth, __last, __comp);
+
   _LIBCPP_DEBUG_RANDOMIZE_RANGE(__first, __nth);
   if (__nth != __last) {
     _LIBCPP_DEBUG_RANDOMIZE_RANGE(++__nth, __last);
   }
 }
 
+template <class _RandomAccessIterator, class _Compare>
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last,
+                 _Compare __comp) {
+  std::__nth_element_impl(std::move(__first), std::move(__nth), std::move(__last), __comp);
+}
+
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last)
-{
-    _VSTD::nth_element(__first, __nth, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last) {
+  std::nth_element(std::move(__first), std::move(__nth), std::move(__last), __less<typename
+      iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/ranges_nth_element.h b/libcxx/include/__algorithm/ranges_nth_element.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_nth_element.h
@@ -0,0 +1,79 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_NTH_ELEMENT_H
+#define _LIBCPP___ALGORITHM_RANGES_NTH_ELEMENT_H
+
+#include <__algorithm/make_projected.h>
+#include <__algorithm/nth_element.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __nth_element {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __nth_element_fn_impl(_Iter __first, _Iter __nth, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto __last_iter = ranges::next(__first, __last);
+
+    auto&& __projected_comp = __make_projected_comp(__comp, __proj);
+    std::__nth_element_impl(std::move(__first), std::move(__nth), __last_iter, __projected_comp);
+
+    return __last_iter;
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Iter __nth, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __nth_element_fn_impl(std::move(__first), std::move(__nth), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, iterator_t<_Range> __nth, _Comp __comp = {},
+                                         _Proj __proj = {}) const {
+    return __nth_element_fn_impl(ranges::begin(__r), std::move(__nth), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __nth_element
+
+inline namespace __cpo {
+  inline constexpr auto nth_element = __nth_element::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_NTH_ELEMENT_H
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -356,6 +356,17 @@
     constexpr borrowed_iterator_t<R>
       ranges::is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});                       // since C++20
 
+  template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});            // since C++20
+
+  template<random_­access_­range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});          // since C++20
+
   template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
            indirect_strict_weak_order<const T*, projected<I, Proj>> Comp = ranges::less>
     constexpr I upper_bound(I first, S last, const T& value, Comp comp = {}, Proj proj = {}); // since C++20
@@ -1196,6 +1207,7 @@
 #include <__algorithm/ranges_minmax_element.h>
 #include <__algorithm/ranges_mismatch.h>
 #include <__algorithm/ranges_none_of.h>
+#include <__algorithm/ranges_nth_element.h>
 #include <__algorithm/ranges_replace.h>
 #include <__algorithm/ranges_replace_if.h>
 #include <__algorithm/ranges_reverse.h>
diff --git a/libcxx/include/module.modulemap.in b/libcxx/include/module.modulemap.in
--- a/libcxx/include/module.modulemap.in
+++ b/libcxx/include/module.modulemap.in
@@ -339,6 +339,7 @@
       module ranges_minmax_element           { private header "__algorithm/ranges_minmax_element.h" }
       module ranges_mismatch                 { private header "__algorithm/ranges_mismatch.h" }
       module ranges_none_of                  { private header "__algorithm/ranges_none_of.h" }
+      module ranges_nth_element              { private header "__algorithm/ranges_nth_element.h" }
       module ranges_replace                  { private header "__algorithm/ranges_replace.h" }
       module ranges_replace_if               { private header "__algorithm/ranges_replace_if.h" }
       module ranges_reverse                  { private header "__algorithm/ranges_reverse.h" }
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
@@ -169,8 +169,8 @@
     //(void)std::ranges::next_permutation(a, Less(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(first, last, UnaryTrue(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(a, UnaryTrue(&copies)); assert(copies == 0);
-    //(void)std::ranges::nth_element(first, mid, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::nth_element(a, mid, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::nth_element(first, mid, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::nth_element(a, mid, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort(first, mid, last, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort(a, mid, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(first, last, first2, mid2, Less(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
@@ -152,8 +152,8 @@
     //(void)std::ranges::next_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(first, last, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(a, UnaryTrue(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::nth_element(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::nth_element(a, mid, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::nth_element(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::nth_element(a, mid, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort(a, mid, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(first, last, first2, mid2, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/private_headers.verify.cpp b/libcxx/test/libcxx/private_headers.verify.cpp
--- a/libcxx/test/libcxx/private_headers.verify.cpp
+++ b/libcxx/test/libcxx/private_headers.verify.cpp
@@ -137,6 +137,7 @@
 #include <__algorithm/ranges_minmax_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_minmax_element.h'}}
 #include <__algorithm/ranges_mismatch.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_mismatch.h'}}
 #include <__algorithm/ranges_none_of.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_none_of.h'}}
+#include <__algorithm/ranges_nth_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_nth_element.h'}}
 #include <__algorithm/ranges_replace.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace.h'}}
 #include <__algorithm/ranges_replace_if.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace_if.h'}}
 #include <__algorithm/ranges_reverse.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_reverse.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.nth.element/ranges_nth_element.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.nth.element/ranges_nth_element.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.nth.element/ranges_nth_element.pass.cpp
@@ -0,0 +1,329 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr I
+//     ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});            // since C++20
+//
+// template<random_­access_­range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr borrowed_iterator_t<R>
+//     ranges::nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});          // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <iterator>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasNthElementIt = requires(Iter first, Iter nth, Sent last, Comp comp) {
+  std::ranges::nth_element(first, nth, last, comp);
+};
+
+static_assert(HasNthElementIt<int*>);
+static_assert(!HasNthElementIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasNthElementIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasNthElementIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasNthElementIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasNthElementIt<int*, int*, BadComparator>);
+static_assert(!HasNthElementIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasNthElementR = requires(Range range, std::ranges::iterator_t<Range> nth, Comp comp) {
+  std::ranges::nth_element(range, nth, comp);
+};
+
+static_assert(HasNthElementR<UncheckedRange<int*>>);
+static_assert(!HasNthElementR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasNthElementR<RandomAccessRangeBadIndex>);
+static_assert(!HasNthElementR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasNthElementR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasNthElementR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasNthElementR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <size_t N, class T, class Iter>
+constexpr void verify_nth(const std::array<T, N>& partially_sorted, size_t nth_index, Iter last,
+    [[maybe_unused]] std::array<T, N> expected) {
+  // Different implementations produce differing output that still satisfies the algorithm requirements, so we can only
+  // check for specific output in the libc++ implementation.
+  LIBCPP_ASSERT(partially_sorted == expected);
+  assert(base(last) == partially_sorted.end());
+
+  auto b = partially_sorted.begin();
+  auto nth = b + nth_index;
+  auto e = partially_sorted.end();
+  if (nth == e)
+    return;
+
+  // All elements on the left are <= nth.
+  assert(std::all_of(b, nth, [&](const auto& v) { return v <= *nth; }));
+  // All elements on the right are >= nth.
+  assert(std::all_of(nth, e, [&](const auto& v) { return v >= *nth; }));
+
+  {
+    auto sorted = partially_sorted;
+    std::ranges::sort(sorted);
+
+    // The element at index `n` is the same as if the range were fully sorted.
+    assert(sorted[nth_index] == *nth);
+  }
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(std::array<int, N> input, size_t nth_index, std::array<int, N> expected) {
+  { // (iterator, sentinel) overload.
+    auto partially_sorted = input;
+    auto b = Iter(partially_sorted.data());
+    auto nth = b + nth_index;
+    auto e = Sent(Iter(partially_sorted.data() + partially_sorted.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::nth_element(b, nth, e);
+    verify_nth(partially_sorted, nth_index, last, expected);
+  }
+
+  { // (range) overload.
+    auto partially_sorted = input;
+    auto b = Iter(partially_sorted.data());
+    auto nth = b + nth_index;
+    auto e = Sent(Iter(partially_sorted.data() + partially_sorted.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::nth_element(range, nth);
+    verify_nth(partially_sorted, nth_index, last, expected);
+  }
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_all_cases(std::array<int, N> input, std::array<std::array<int, N>, N> expected_array) {
+  for (int n = 0; n != N; ++n) {
+    test_one<Iter, Sent, N>(input, n, expected_array[n]);
+  }
+  test_one<Iter, Sent, N>(input, N, input);
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_all_cases(std::array<int, N> input, std::array<int, N> expected) {
+  for (int n = 0; n != N; ++n) {
+    test_one<Iter, Sent, N>(input, n, expected);
+  }
+  test_one<Iter, Sent, N>(input, N, input);
+}
+
+template <class Iter, class Sent>
+constexpr void test_iterators_2() {
+  { // Empty sequence.
+    test_one<Iter, Sent, 0>({}, 0, {});
+  }
+
+  { // 1-element sequence.
+    test_one<Iter, Sent, 1>({1}, 0, {1});
+    test_one<Iter, Sent, 1>({1}, 1, {1});
+  }
+
+  { // 3-element sequence.
+    std::array input = {2, 1};
+    std::array expected = {1, 2};
+    test_all_cases<Iter, Sent>(input, expected);
+  }
+
+  { // 3-element sequence.
+    std::array input = {2, 1, 3};
+    std::array expected = {1, 2, 3};
+    test_all_cases<Iter, Sent>(input, expected);
+  }
+
+  { // Longer sequence.
+    std::array input = {2, 1, 3, 6, 8, 4, 11, 5};
+    std::array expected1 = {1, 2, 3, 4, 5, 6, 11, 8};
+    std::array expected2 = {2, 1, 3, 4, 5, 6, 11, 8};
+    std::array expected3 = {2, 1, 3, 4, 5, 6, 8, 11};
+
+    std::array<decltype(input), input.size()> expected_array = {
+      expected1, expected1, expected1, expected1, expected2, expected3, expected3, expected3
+    };
+
+    test_all_cases<Iter, Sent>(input, expected_array);
+  }
+
+  { // Longer sequence with duplicates.
+    std::array input = {2, 1, 3, 6, 2, 8, 6};
+    std::array expected = {1, 2, 2, 3, 6, 6, 8};
+    test_all_cases<Iter, Sent>(input, expected);
+  }
+
+  { // All elements are the same.
+    std::array input = {1, 1, 1, 1};
+    test_all_cases<Iter, Sent>(input, input);
+  }
+
+  { // nth element is in the right place.
+    std::array input = {6, 5, 3, 1, 4, 2};
+    std::array expected = {1, 2, 3, 4, 5, 6};
+    constexpr size_t N = input.size();
+
+    test_one<Iter, Sent, N>(input, 2, expected);
+  }
+
+  { // Already sorted.
+    std::array input = {1, 2, 3, 4, 5, 6};
+    test_all_cases<Iter, Sent>(input, input);
+  }
+
+  { // Reverse sorted.
+    std::array input = {6, 5, 4, 3, 2, 1};
+    std::array expected = {1, 2, 3, 4, 5, 6};
+    test_all_cases<Iter, Sent>(input, expected);
+  }
+
+  { // Repeating pattern.
+    std::array input = {2, 1, 2, 1, 2, 1};
+    std::array expected = {1, 1, 1, 2, 2, 2};
+    test_all_cases<Iter, Sent>(input, expected);
+  }
+}
+
+template <class Iter>
+constexpr void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+constexpr void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array input = {1, 2, 3, 4, 5};
+    std::array expected = {5, 4, 3, 2, 1};
+    std::ranges::greater comp;
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in.begin(), in.begin() + 1, in.end(), comp);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in, in.begin() + 1, comp);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr bool operator==(const A&) const = default;
+    };
+
+    const std::array input = {A{2}, A{1}, A{3}};
+    std::array expected = {A{1}, A{2}, A{3}};
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in.begin(), in.begin() + 1, in.end(), {}, &A::a);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in, in.begin() + 1, {}, &A::a);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct S {
+      int i;
+      constexpr S(int i_) : i(i_) {}
+
+      constexpr bool comparator(const S& rhs) const { return i < rhs.i; }
+      constexpr const S& projection() const { return *this; }
+
+      constexpr bool operator==(const S&) const = default;
+    };
+
+    const std::array input = {S{2}, S{1}, S{3}};
+    std::array expected = {S{1}, S{2}, S{3}};
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in.begin(), in.begin() + 1, in.end(), &S::comparator, &S::projection);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::nth_element(in, in.begin() + 1, &S::comparator, &S::projection);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array input = {2, 1, 3};
+    std::array expected = {1, 2, 3};
+    auto pred = [](int i, int j) { return BooleanTestable{i < j}; };
+
+    {
+      std::array in = input;
+      auto last = std::ranges::nth_element(in.begin(), in.begin() + 1, in.end(), pred);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      std::array in = input;
+      auto last = std::ranges::nth_element(in, in.begin() + 1, pred);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::nth_element(std::array{1, 2, 3}, 0);
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
--- a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
+++ b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
@@ -108,7 +108,7 @@
 //static_assert(test(std::ranges::move_backward, a, a));
 //static_assert(test(std::ranges::next_permutation, a));
 static_assert(test(std::ranges::none_of, a, odd));
-//static_assert(test(std::ranges::nth_element, a, a+5));
+static_assert(test(std::ranges::nth_element, a, a+5));
 //static_assert(test(std::ranges::partial_sort, a, a+5));
 //static_assert(test(std::ranges::partial_sort_copy, a, a));
 //static_assert(test(std::ranges::partition, a, odd));