diff --git a/core/scripts/run-tests.sh b/core/scripts/run-tests.sh
index fdc5157292471e85293d994e0b78a5f6971fb398..41495c779eb47d74a1c7e8252e837cefb57cb06a 100755
--- a/core/scripts/run-tests.sh
+++ b/core/scripts/run-tests.sh
@@ -474,23 +474,6 @@ function simpletest_script_init() {
     exit(SIMPLETEST_SCRIPT_EXIT_FAILURE);
   }
 
-  // Detect if we're in the top-level process using the private 'execute-test'
-  // argument. Determine if being run on drupal.org's testing infrastructure
-  // using the presence of 'drupaltestbot' in the database url.
-  // @todo https://www.drupal.org/project/drupalci_testbot/issues/2860941 Use
-  //   better environment variable to detect DrupalCI.
-  // @todo https://www.drupal.org/project/drupal/issues/2942473 Remove when
-  //   dropping PHPUnit 4 and PHP 5 support.
-  if (!$args['execute-test'] && preg_match('/drupalci/', $args['sqlite'])) {
-    // Update PHPUnit if needed and possible. There is a later check once the
-    // autoloader is in place to ensure we're on the correct version. We need to
-    // do this before the autoloader is in place to ensure that it is correct.
-    $composer = ($composer = rtrim('\\' === DIRECTORY_SEPARATOR ? preg_replace('/[\r\n].*/', '', `where.exe composer.phar`) : `which composer.phar`))
-      ? $php . ' ' . escapeshellarg($composer)
-      : 'composer';
-    passthru("$composer run-script drupal-phpunit-upgrade-check");
-  }
-
   $autoloader = require_once __DIR__ . '/../../autoload.php';
 
   // Get URL from arguments.
diff --git a/core/tests/README.md b/core/tests/README.md
index 4682b065c173ded06d99222c3f22ffb5a0bbd47e..e075af7fd981860e80e8764f7a97266e1be0a466 100644
--- a/core/tests/README.md
+++ b/core/tests/README.md
@@ -74,8 +74,6 @@ chromedriver using port 4444, and keep it running:
 
 * Ensure your vendor directory is populated
   (e.g. by running `composer install`)
-* If you're running PHP 7.0 or greater you will need to upgrade PHPUnit with
-  `composer run-script drupal-phpunit-upgrade`
 * Install [Node.js](https://nodejs.org/en/download/) and
   [yarn](https://yarnpkg.com/en/docs/install). The versions required are
   specificed inside core/package.json in the `engines` field