diff --git a/CMakeLists.txt b/CMakeLists.txt
index f648f2299..efe3cab65 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -16,7 +16,9 @@
 #   mbedtls, mbedx509, mbedcrypto and apidoc targets.
 #
 
-cmake_minimum_required(VERSION 2.8.12)
+# We specify a minimum requirement of 3.10.2, but for now use 3.5.1 here
+# until our infrastructure catches up.
+cmake_minimum_required(VERSION 3.5.1)
 
 # https://cmake.org/cmake/help/latest/policy/CMP0011.html
 # Setting this policy is required in CMake >= 3.18.0, otherwise a warning is generated. The OLD
diff --git a/ChangeLog.d/tool-versions.txt b/ChangeLog.d/tool-versions.txt
new file mode 100644
index 000000000..b89b384aa
--- /dev/null
+++ b/ChangeLog.d/tool-versions.txt
@@ -0,0 +1,4 @@
+Requirement changes
+   * Refresh the minimum supported versions of tools to build the
+     library. CMake versions older than 3.10.2 and Python older
+     than 3.6 are no longer supported.
diff --git a/README.md b/README.md
index 3f41a0d76..78d3c30cf 100644
--- a/README.md
+++ b/README.md
@@ -26,7 +26,7 @@ Documentation for the Mbed TLS interfaces in the default library configuration i
 
 To generate a local copy of the library documentation in HTML format, tailored to your compile-time configuration:
 
-1. Make sure that [Doxygen](http://www.doxygen.nl/) is installed. We use version 1.8.11 but slightly older or more recent versions should work.
+1. Make sure that [Doxygen](http://www.doxygen.nl/) is installed.
 1. Run `make apidoc`.
 1. Browse `apidoc/index.html` or `apidoc/modules.html`.
 
@@ -39,7 +39,7 @@ There are currently three active build systems used within Mbed TLS releases:
 
 -   GNU Make
 -   CMake
--   Microsoft Visual Studio (Microsoft Visual Studio 2013 or later)
+-   Microsoft Visual Studio
 
 The main systems used for development are CMake and GNU Make. Those systems are always complete and up-to-date. The others should reflect all changes present in the CMake and Make build system, although features may not be ported there automatically.
 
@@ -49,10 +49,13 @@ The Make and CMake build systems create three libraries: libmbedcrypto, libmbedx
 
 You need the following tools to build the library with the provided makefiles:
 
-* GNU Make or a build tool that CMake supports.
-* A C99 toolchain (compiler, linker, archiver). We actively test with GCC 5.4, Clang 3.8, IAR8 and Visual Studio 2013. More recent versions should work. Slightly older versions may work.
-* Python 3 to generate the test code, and to generate sample programs in the development branch.
+* GNU Make 3.82 or a build tool that CMake supports.
+* A C99 toolchain (compiler, linker, archiver). We actively test with GCC 5.4, Clang 3.8, IAR 8 and Visual Studio 2013. More recent versions should work. Slightly older versions may work.
+* Python 3.6 to generate the test code, and to generate sample programs in the development branch.
 * Perl to run the tests, and to generate some source files in the development branch.
+* CMake 3.10.2 or later (if using CMake).
+* Microsoft Visual Studio 2013 or later (if using Visual Studio).
+* Doxygen 1.8.11 or later (if building the documentation; slightly older versions should work).
 
 ### Generated source files in the development branch