CakePHP and Twilio are used together to receive and reply to SMS messages. The process involves setting up a Twilio number, creating a TwiML application, and configuring CakePHP to handle the requests. This includes adding a line to the `app/Config/core.php` file to set the 'twilio' prefix, another line to the `app/Config/routes.php` file to parse the '.xml' extension, and creating an action in the `InstallationsController.php` file to receive and process the SMS messages. The action checks for a POST request, finds the correct installation using the Twilio phone number, creates a message array, saves it to the database, and sends a response with a 'Thank you!' message.