diff --git a/libcxx/include/__iterator/concepts.h b/libcxx/include/__iterator/concepts.h
--- a/libcxx/include/__iterator/concepts.h
+++ b/libcxx/include/__iterator/concepts.h
@@ -127,7 +127,17 @@
   incrementable<_Ip> &&
   sentinel_for<_Ip, _Ip>;
 
-// clang-format on
+// [iterator.concept.bidir]
+template<class _Ip>
+concept bidirectional_iterator =
+  forward_iterator<_Ip> &&
+  derived_from<_ITER_CONCEPT<_Ip>, bidirectional_iterator_tag> &&
+  requires(_Ip __i) {
+    { --__i } -> same_as<_Ip&>;
+    { __i-- } -> same_as<_Ip>;
+  };
+
+  // clang-format on
 
 #endif // !defined(_LIBCPP_HAS_NO_RANGES)
 
diff --git a/libcxx/include/__ranges/concepts.h b/libcxx/include/__ranges/concepts.h
--- a/libcxx/include/__ranges/concepts.h
+++ b/libcxx/include/__ranges/concepts.h
@@ -58,8 +58,10 @@
   concept forward_range = input_range<_Tp> && forward_iterator<iterator_t<_Tp> >;
 
   template <class _Tp>
-  concept common_range = range<_Tp> && same_as<iterator_t<_Tp>, sentinel_t<_Tp> >;
+  concept bidirectional_range = forward_range<_Tp> && bidirectional_iterator<iterator_t<_Tp> >;
 
+  template <class _Tp>
+  concept common_range = range<_Tp> && same_as<iterator_t<_Tp>, sentinel_t<_Tp> >;
 } // namespace ranges
 
 #endif // !defined(_LIBCPP_HAS_NO_RANGES)
diff --git a/libcxx/include/iterator b/libcxx/include/iterator
--- a/libcxx/include/iterator
+++ b/libcxx/include/iterator
@@ -83,6 +83,10 @@
 template<class I>
   concept forward_iterator = see below;                    // since C++20
 
+// [iterator.concept.bidir], concept bidirectional_iterator
+template<class I>
+  concept bidirectional_­iterator = see below;              // since C++20
+
 template<class Category, class T, class Distance = ptrdiff_t,
          class Pointer = T*, class Reference = T&>
 struct iterator
diff --git a/libcxx/include/ranges b/libcxx/include/ranges
--- a/libcxx/include/ranges
+++ b/libcxx/include/ranges
@@ -54,6 +54,9 @@
   template<class T>
     concept forward_range = see below;
 
+  template<class T>
+  concept bidirectional_­range = see below;
+
   template <class _Tp>
     concept common_range = see below;
 }
diff --git a/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/associative/multimap/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/associative/multimap/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/associative/multimap/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/associative/multimap/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/associative/multiset/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/associative/multiset/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/associative/multiset/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/associative/multiset/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/array/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/array/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/array/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/array/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/deque/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/deque/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/deque/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/deque/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/forwardlist/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/forwardlist/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/forwardlist/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/forwardlist/range_concept_conformance.compile.pass.cpp
@@ -24,7 +24,9 @@
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
 static_assert(stdr::forward_range<range>);
+static_assert(!stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
 static_assert(stdr::forward_range<range const>);
+static_assert(!stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/list/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/list/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/list/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/list/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/vector.bool/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/vector.bool/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/vector.bool/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/vector.bool/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/sequences/vector/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/sequences/vector/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/sequences/vector/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/sequences/vector/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/unord/unord.map/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/unord/unord.map/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/unord/unord.map/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/unord/unord.map/range_concept_conformance.compile.pass.cpp
@@ -24,7 +24,9 @@
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
 static_assert(stdr::forward_range<range>);
+static_assert(!stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
 static_assert(stdr::forward_range<range const>);
+static_assert(!stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/unord/unord.multimap/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/unord/unord.multimap/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/unord/unord.multimap/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/unord/unord.multimap/range_concept_conformance.compile.pass.cpp
@@ -24,7 +24,9 @@
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
 static_assert(stdr::forward_range<range>);
+static_assert(!stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
 static_assert(stdr::forward_range<range const>);
+static_assert(!stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/unord/unord.multiset/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/unord/unord.multiset/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/unord/unord.multiset/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/unord/unord.multiset/range_concept_conformance.compile.pass.cpp
@@ -24,7 +24,9 @@
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
 static_assert(stdr::forward_range<range>);
+static_assert(!stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
 static_assert(stdr::forward_range<range const>);
+static_assert(!stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/unord/unord.set/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/unord/unord.set/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/unord/unord.set/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/unord/unord.set/range_concept_conformance.compile.pass.cpp
@@ -24,7 +24,9 @@
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
 static_assert(stdr::forward_range<range>);
+static_assert(!stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
 static_assert(stdr::common_range<range const>);
 static_assert(stdr::forward_range<range const>);
+static_assert(!stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/containers/views/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/containers/views/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/containers/views/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/containers/views/range_concept_conformance.compile.pass.cpp
@@ -23,8 +23,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
 static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+static_assert(stdr::bidirectional_range<range>);
 
 static_assert(std::same_as<stdr::iterator_t<range const>, range::iterator>);
 static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(stdr::bidirectional_range<range const>);
diff --git a/libcxx/test/std/input.output/filesystems/class.path/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/input.output/filesystems/class.path/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/input.output/filesystems/class.path/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/input.output/filesystems/class.path/range_concept_conformance.compile.pass.cpp
@@ -22,8 +22,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<fs::path>, fs::path::iterator>);
 static_assert(stdr::common_range<fs::path>);
-static_assert(stdr::forward_range<fs::path>);
+static_assert(stdr::bidirectional_range<fs::path>);
 
 static_assert(std::same_as<stdr::iterator_t<fs::path const>, fs::path::const_iterator>);
 static_assert(stdr::common_range<fs::path const>);
-static_assert(stdr::forward_range<fs::path const>);
+static_assert(stdr::bidirectional_range<fs::path const>);
diff --git a/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp
@@ -0,0 +1,150 @@
+//===----------------------------------------------------------------------===//
+//
+// 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-no-concepts
+// UNSUPPORTED: gcc-10
+// XFAIL: msvc && clang
+
+// template<class T>
+// concept bidirectional_iterator;
+
+#include <iterator>
+
+#include <concepts>
+
+#include "test_iterators.h"
+
+static_assert(!std::bidirectional_iterator<input_iterator<int*> >);
+static_assert(!std::bidirectional_iterator<cpp20_input_iterator<int*> >);
+static_assert(!std::bidirectional_iterator<forward_iterator<int*> >);
+static_assert(std::bidirectional_iterator<bidirectional_iterator<int*> >);
+static_assert(std::bidirectional_iterator<random_access_iterator<int*> >);
+static_assert(std::bidirectional_iterator<contiguous_iterator<int*> >);
+
+
+static_assert(std::bidirectional_iterator<int*>);
+static_assert(std::bidirectional_iterator<int const*>);
+static_assert(std::bidirectional_iterator<int volatile*>);
+static_assert(std::bidirectional_iterator<int const volatile*>);
+
+struct not_forward_iterator {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type operator*() const;
+
+  not_forward_iterator& operator++();
+  not_forward_iterator operator++(int);
+
+  not_forward_iterator& operator--();
+  not_forward_iterator& operator--(int);
+};
+static_assert(std::input_iterator<not_forward_iterator> && !std::forward_iterator<not_forward_iterator> &&
+              !std::bidirectional_iterator<not_forward_iterator>);
+
+struct wrong_iterator_category {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_category = std::forward_iterator_tag;
+
+  value_type& operator*() const;
+
+  wrong_iterator_category& operator++();
+  wrong_iterator_category operator++(int);
+
+  wrong_iterator_category& operator--();
+  wrong_iterator_category operator--(int);
+
+  bool operator==(wrong_iterator_category const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<wrong_iterator_category>);
+
+struct wrong_iterator_concept {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::forward_iterator_tag;
+
+  value_type& operator*() const;
+
+  wrong_iterator_concept& operator++();
+  wrong_iterator_concept operator++(int);
+
+  wrong_iterator_concept& operator--();
+  wrong_iterator_concept operator--(int);
+
+  bool operator==(wrong_iterator_concept const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<wrong_iterator_concept>);
+
+struct no_predecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  no_predecrement& operator++();
+  no_predecrement operator++(int);
+
+  no_predecrement operator--(int);
+
+  bool operator==(no_predecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<no_predecrement>);
+
+struct bad_predecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  bad_predecrement& operator++();
+  bad_predecrement operator++(int);
+
+  bad_predecrement operator--();
+  bad_predecrement operator--(int);
+
+  bool operator==(bad_predecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<bad_predecrement>);
+
+struct no_postdecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  no_postdecrement& operator++();
+  no_postdecrement operator++(int);
+
+  no_postdecrement& operator--();
+
+  bool operator==(no_postdecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<no_postdecrement>);
+
+struct bad_postdecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  bad_postdecrement& operator++();
+  bad_postdecrement operator++(int);
+
+  bad_postdecrement& operator--();
+  bad_postdecrement& operator--(int);
+
+  bool operator==(bad_postdecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<bad_postdecrement>);
diff --git a/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp
copy from libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp
copy to libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp
--- a/libcxx/test/std/containers/associative/map/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp
@@ -11,20 +11,24 @@
 // UNSUPPORTED: gcc-10
 // XFAIL: msvc && clang
 
-// map
+// template<class T>
+// concept bidirectional_iterator;
 
-#include <map>
+#include <iterator>
 
 #include <concepts>
-#include <ranges>
 
-using range = std::map<int, int>;
-namespace stdr = std::ranges;
+// clang-format off
+template<std::forward_iterator I>
+requires std::derived_from<std::_ITER_CONCEPT<I>, std::bidirectional_iterator_tag>
+[[nodiscard]] constexpr bool check_subsumption() {
+  return false;
+}
 
-static_assert(std::same_as<stdr::iterator_t<range>, range::iterator>);
-static_assert(stdr::common_range<range>);
-static_assert(stdr::forward_range<range>);
+template<std::bidirectional_iterator>
+[[nodiscard]] constexpr bool check_subsumption() {
+  return true;
+}
+// clang-format on
 
-static_assert(std::same_as<stdr::iterator_t<range const>, range::const_iterator>);
-static_assert(stdr::common_range<range const>);
-static_assert(stdr::forward_range<range const>);
+static_assert(check_subsumption<int*>());
diff --git a/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.forward/forward_iterator.compile.pass.cpp b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.forward/forward_iterator.compile.pass.cpp
--- a/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.forward/forward_iterator.compile.pass.cpp
+++ b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.forward/forward_iterator.compile.pass.cpp
@@ -19,13 +19,13 @@
 
 #include "test_iterators.h"
 
+static_assert(!std::forward_iterator<input_iterator<int*> >);
+static_assert(!std::forward_iterator<cpp20_input_iterator<int*> >);
 static_assert(std::forward_iterator<forward_iterator<int*> >);
 static_assert(std::forward_iterator<bidirectional_iterator<int*> >);
 static_assert(std::forward_iterator<random_access_iterator<int*> >);
 static_assert(std::forward_iterator<contiguous_iterator<int*> >);
 
-// TODO: add new `cxx20_*_iterator`s as they're added
-static_assert(!std::forward_iterator<cpp20_input_iterator<int*> >);
 
 static_assert(std::forward_iterator<int*>);
 static_assert(std::forward_iterator<int const*>);
diff --git a/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp b/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp
@@ -0,0 +1,41 @@
+//===----------------------------------------------------------------------===//
+//
+// 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-no-concepts
+// UNSUPPORTED: gcc-10
+// XFAIL: msvc && clang
+
+// template<range _Rp>
+// concept bidirectional_range;
+
+#include <ranges>
+
+#include "test_range.h"
+
+namespace stdr = std::ranges;
+
+template <template <class...> class I>
+constexpr bool check_bidirectional_range() {
+  constexpr bool result = stdr::bidirectional_range<test_range<I> >;
+  static_assert(stdr::bidirectional_range<test_range<I> const> == result);
+  static_assert(stdr::bidirectional_range<test_non_const_common_range<I> > == result);
+  static_assert(stdr::bidirectional_range<test_non_const_range<I> > == result);
+  static_assert(stdr::bidirectional_range<test_common_range<I> > == result);
+  static_assert(stdr::bidirectional_range<test_common_range<I> const> == result);
+  static_assert(!stdr::bidirectional_range<test_non_const_common_range<I> const>);
+  static_assert(!stdr::bidirectional_range<test_non_const_range<I> const>);
+  return result;
+}
+
+static_assert(!check_bidirectional_range<input_iterator>());
+static_assert(!check_bidirectional_range<cpp20_input_iterator>());
+static_assert(!check_bidirectional_range<forward_iterator>());
+static_assert(check_bidirectional_range<bidirectional_iterator>());
+static_assert(check_bidirectional_range<random_access_iterator>());
+static_assert(check_bidirectional_range<contiguous_iterator>());
diff --git a/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp b/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
--- a/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
+++ b/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
@@ -56,3 +56,19 @@
 // clang-format on
 
 static_assert(check_forward_range_subsumption<range>());
+
+// clang-format off
+template<std::ranges::forward_range R>
+requires std::bidirectional_iterator<std::ranges::iterator_t<R> >
+[[nodiscard]] constexpr bool check_bidirectional_range_subsumption() {
+  return false;
+}
+
+template<std::ranges::bidirectional_range>
+requires true
+[[nodiscard]] constexpr bool check_bidirectional_range_subsumption() {
+  return true;
+}
+// clang-format on
+
+static_assert(check_bidirectional_range_subsumption<range>());
diff --git a/libcxx/test/std/re/re.results/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/re/re.results/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/re/re.results/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/re/re.results/range_concept_conformance.compile.pass.cpp
@@ -22,8 +22,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<std::cmatch>, std::cmatch::iterator>);
 static_assert(stdr::common_range<std::cmatch>);
-static_assert(stdr::forward_range<std::cmatch>);
+static_assert(stdr::bidirectional_range<std::cmatch>);
 
 static_assert(std::same_as<stdr::iterator_t<std::cmatch const>, std::cmatch::const_iterator>);
 static_assert(stdr::common_range<std::cmatch const>);
-static_assert(stdr::forward_range<std::cmatch const>);
+static_assert(stdr::bidirectional_range<std::cmatch const>);
diff --git a/libcxx/test/std/strings/basic.string/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/strings/basic.string/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/strings/basic.string/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/strings/basic.string/range_concept_conformance.compile.pass.cpp
@@ -22,8 +22,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<std::string>, std::string::iterator>);
 static_assert(stdr::common_range<std::string>);
-static_assert(stdr::forward_range<std::string>);
+static_assert(stdr::bidirectional_range<std::string>);
 
 static_assert(std::same_as<stdr::iterator_t<std::string const>, std::string::const_iterator>);
 static_assert(stdr::common_range<std::string const>);
-static_assert(stdr::forward_range<std::string const>);
+static_assert(stdr::bidirectional_range<std::string const>);
diff --git a/libcxx/test/std/strings/string.view/range_concept_conformance.compile.pass.cpp b/libcxx/test/std/strings/string.view/range_concept_conformance.compile.pass.cpp
--- a/libcxx/test/std/strings/string.view/range_concept_conformance.compile.pass.cpp
+++ b/libcxx/test/std/strings/string.view/range_concept_conformance.compile.pass.cpp
@@ -22,8 +22,8 @@
 
 static_assert(std::same_as<stdr::iterator_t<std::string_view>, std::string_view::iterator>);
 static_assert(stdr::common_range<std::string_view>);
-static_assert(stdr::forward_range<std::string_view>);
+static_assert(stdr::bidirectional_range<std::string_view>);
 
 static_assert(std::same_as<stdr::iterator_t<std::string_view const>, std::string_view::const_iterator>);
 static_assert(stdr::common_range<std::string_view const>);
-static_assert(stdr::forward_range<std::string_view const>);
+static_assert(stdr::bidirectional_range<std::string_view const>);
diff --git a/libcxx/test/support/test_iterators.h b/libcxx/test/support/test_iterators.h
--- a/libcxx/test/support/test_iterators.h
+++ b/libcxx/test/support/test_iterators.h
@@ -695,6 +695,46 @@
   I base_ = I();
 };
 
+template <class I>
+struct cxx20_bidirectional_iterator {
+  using value_type = std::iter_value_t<I>;
+  using difference_type = std::iter_difference_t<I>;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  cxx20_bidirectional_iterator() = default;
+
+  explicit constexpr cxx20_bidirectional_iterator(I base) : base_(std::move(base)) {}
+
+  constexpr decltype(auto) operator*() const { return *base_; }
+
+  cxx20_bidirectional_iterator& operator++() {
+    ++base_;
+    return *this;
+  }
+
+  cxx20_bidirectional_iterator operator++(int) {
+    auto temp = *this;
+    ++*this;
+    return *this;
+  }
+
+  cxx20_bidirectional_iterator& operator--() {
+    --base_;
+    return *this;
+  }
+
+  cxx20_bidirectional_iterator operator--(int) {
+    auto temp = *this;
+    --*this;
+    return *this;
+  }
+
+  bool operator==(cxx20_bidirectional_iterator const&) const = default;
+
+private:
+  I base_ = I();
+};
+
 #endif // TEST_STD_VER > 17 && defined(__cpp_lib_concepts)
 
 #undef DELETE_FUNCTION