Test automation with PHP Codeception allows testing of applications like Joomla using the Codeception testing framework. Codeception is a full-stack PHP testing framework inspired by behavior-driven development. It provides new ways of writing acceptance, functional, and unit tests, powered by PHPUnit. The document demonstrates how to install Codeception via its PHAR file, create an acceptance test to automate the Joomla backend login process, and run the test. Key steps include bootstrapping Codeception, generating a test file, adding test code to log in and assert success, and running the test from the command line.