diff --git a/libcxx/include/__config b/libcxx/include/__config
--- a/libcxx/include/__config
+++ b/libcxx/include/__config
@@ -114,6 +114,8 @@
 #  define _LIBCPP_ABI_DO_NOT_EXPORT_BASIC_STRING_COMMON
 // Remove vector base class
 #  define _LIBCPP_ABI_DO_NOT_EXPORT_VECTOR_BASE_COMMON
+// According to the Standard, `bitset::operator[] const` returns bool
+#  define _LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL
 #elif _LIBCPP_ABI_VERSION == 1
 #  if !defined(_LIBCPP_OBJECT_FORMAT_COFF)
 // Enable compiling copies of now inline methods into the dylib to support
diff --git a/libcxx/include/bitset b/libcxx/include/bitset
--- a/libcxx/include/bitset
+++ b/libcxx/include/bitset
@@ -714,9 +714,12 @@
     bitset& flip(size_t __pos);
 
     // element access:
-    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
-                              const_reference operator[](size_t __p) const {return base::__make_ref(__p);}
-    _LIBCPP_INLINE_VISIBILITY       reference operator[](size_t __p)       {return base::__make_ref(__p);}
+#ifdef _LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR            bool operator[](size_t __p) const {return base::__make_ref(__p);}
+#else
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR const_reference operator[](size_t __p) const {return base::__make_ref(__p);}
+#endif
+    _LIBCPP_HIDE_FROM_ABI                         reference operator[](size_t __p)       {return base::__make_ref(__p);}
     _LIBCPP_INLINE_VISIBILITY
     unsigned long to_ulong() const;
     _LIBCPP_INLINE_VISIBILITY
diff --git a/libcxx/include/vector b/libcxx/include/vector
--- a/libcxx/include/vector
+++ b/libcxx/include/vector
@@ -2077,7 +2077,11 @@
     __compressed_pair<size_type, __storage_allocator> __cap_alloc_;
 public:
     typedef __bit_reference<vector>                  reference;
+#ifdef _LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL
+    using const_reference = bool;
+#else
     typedef __bit_const_reference<vector>            const_reference;
+#endif
 private:
     _LIBCPP_INLINE_VISIBILITY
     size_type& __cap() _NOEXCEPT
diff --git a/libcxx/test/std/containers/sequences/vector.bool/const_reference.pass.cpp b/libcxx/test/std/containers/sequences/vector.bool/const_reference.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/containers/sequences/vector.bool/const_reference.pass.cpp
@@ -0,0 +1,37 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// <vector>
+
+#include <cassert>
+#include <vector>
+
+#include "test_macros.h"
+
+bool test() {
+  using CRefT = std::vector<bool>::const_reference;
+#if !defined(_LIBCPP_VERSION) || defined(_LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL)
+  ASSERT_SAME_TYPE(CRefT, bool);
+#else
+  ASSERT_SAME_TYPE(CRefT, std::__bit_const_reference<std::vector<bool>>);
+  std::vector<bool> vec;
+  vec.push_back(true);
+  CRefT ref = vec[0];
+  assert(ref);
+  vec[0] = false;
+  assert(!ref);
+#endif
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+
+  return 0;
+}
diff --git a/libcxx/test/std/utilities/template.bitset/bitset.members/index.pass.cpp b/libcxx/test/std/utilities/template.bitset/bitset.members/index.pass.cpp
--- a/libcxx/test/std/utilities/template.bitset/bitset.members/index.pass.cpp
+++ b/libcxx/test/std/utilities/template.bitset/bitset.members/index.pass.cpp
@@ -42,6 +42,7 @@
             assert(r == false);
             assert(v1.test(N/2) == false);
         }
+        ASSERT_SAME_TYPE(decltype(v1[0]), typename std::bitset<N>::reference);
     }
 }
 
@@ -56,5 +57,11 @@
     test_index<65>();
     test_index<1000>();
 
+    std::bitset<1> set;
+    set[0] = false;
+    auto b = set[0];
+    set[0] = true;
+    assert(b);
+
     return 0;
 }
diff --git a/libcxx/test/std/utilities/template.bitset/bitset.members/index_const.pass.cpp b/libcxx/test/std/utilities/template.bitset/bitset.members/index_const.pass.cpp
--- a/libcxx/test/std/utilities/template.bitset/bitset.members/index_const.pass.cpp
+++ b/libcxx/test/std/utilities/template.bitset/bitset.members/index_const.pass.cpp
@@ -25,6 +25,11 @@
             assert(v[N/2] == v.test(N/2));
         }
     }
+#if !defined(_LIBCPP_VERSION) || defined(_LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL)
+    ASSERT_SAME_TYPE(decltype(cases[0][0]), bool);
+#else
+    ASSERT_SAME_TYPE(decltype(cases[0][0]), typename std::bitset<N>::const_reference);
+#endif
 }
 
 int main(int, char**) {
@@ -38,5 +43,16 @@
     test_index_const<65>();
     test_index_const<1000>();
 
+  std::bitset<1> set_;
+  set_[0] = false;
+  const auto& set = set_;
+  auto b = set[0];
+  set_[0] = true;
+#if !defined(_LIBCPP_VERSION) || defined(_LIBCPP_ABI_BITSET_VECTOR_BOOL_CONST_SUBSCRIPT_RETURN_BOOL)
+  assert(!b);
+#else
+  assert(b);
+#endif
+
     return 0;
 }