diff --git a/libcxx/docs/index.rst b/libcxx/docs/index.rst
--- a/libcxx/docs/index.rst
+++ b/libcxx/docs/index.rst
@@ -103,7 +103,7 @@
 ============ =============== ========================== =====================
 Compiler     Versions        Restrictions               Support policy
 ============ =============== ========================== =====================
-Clang        11, 12                                     latest two stable releases per `LLVM's release page <https://releases.llvm.org>`_
+Clang        12, 13                                     latest two stable releases per `LLVM's release page <https://releases.llvm.org>`_
 AppleClang   12                                         latest stable release per `Xcode's release page <https://developer.apple.com/documentation/xcode-release-notes>`_
 GCC          11              In C++11 or later only     latest stable release per `GCC's release page <https://gcc.gnu.org/releases.html>`_
 ============ =============== ========================== =====================
diff --git a/libcxx/utils/ci/Dockerfile b/libcxx/utils/ci/Dockerfile
--- a/libcxx/utils/ci/Dockerfile
+++ b/libcxx/utils/ci/Dockerfile
@@ -55,7 +55,7 @@
 RUN locale-gen
 
 # Install Clang <latest>, <latest-1> and ToT, which are the ones we support.
-ENV LLVM_LATEST_VERSION=12
+ENV LLVM_LATEST_VERSION=13
 RUN apt-get update && apt-get install -y lsb-release wget software-properties-common
 RUN wget https://apt.llvm.org/llvm.sh -O /tmp/llvm.sh
 RUN bash /tmp/llvm.sh $(($LLVM_LATEST_VERSION - 1)) # previous release
diff --git a/libcxx/utils/ci/buildkite-pipeline.yml b/libcxx/utils/ci/buildkite-pipeline.yml
--- a/libcxx/utils/ci/buildkite-pipeline.yml
+++ b/libcxx/utils/ci/buildkite-pipeline.yml
@@ -174,8 +174,8 @@
           limit: 2
     timeout_in_minutes: 120
 
-  - label: "Clang 11"
-    command: "libcxx/utils/ci/run-buildbot generic-clang-11"
+  - label: "Clang 12"
+    command: "libcxx/utils/ci/run-buildbot generic-clang-12"
     artifact_paths:
       - "**/test-results.xml"
     agents:
@@ -187,8 +187,8 @@
           limit: 2
     timeout_in_minutes: 120
 
-  - label: "Clang 12"
-    command: "libcxx/utils/ci/run-buildbot generic-clang-12"
+  - label: "Clang 13"
+    command: "libcxx/utils/ci/run-buildbot generic-clang-13"
     artifact_paths:
       - "**/test-results.xml"
     agents:
diff --git a/libcxx/utils/ci/run-buildbot b/libcxx/utils/ci/run-buildbot
--- a/libcxx/utils/ci/run-buildbot
+++ b/libcxx/utils/ci/run-buildbot
@@ -288,17 +288,17 @@
                    -DLIBUNWIND_TEST_CONFIG="llvm-libunwind-shared.cfg.in"
     check-runtimes
 ;;
-generic-clang-11)
-    export CC=clang-11
-    export CXX=clang++-11
+generic-clang-12)
+    export CC=clang-12
+    export CXX=clang++-12
     clean
     generate-cmake -DLIBCXX_TEST_CONFIG="llvm-libc++-shared.cfg.in" \
                    -DLIBUNWIND_TEST_CONFIG="llvm-libunwind-shared.cfg.in"
     check-runtimes
 ;;
-generic-clang-12)
-    export CC=clang-12
-    export CXX=clang++-12
+generic-clang-13)
+    export CC=clang-13
+    export CXX=clang++-13
     clean
     generate-cmake -DLIBCXX_TEST_CONFIG="llvm-libc++-shared.cfg.in" \
                    -DLIBUNWIND_TEST_CONFIG="llvm-libunwind-shared.cfg.in"