PHP has several built-in functions for connecting to and manipulating MySQL databases, including mysqli_connect() to establish a connection, mysqli_select_db() to select a database, mysqli_query() to execute SQL queries, mysqli_num_rows() to get the number of rows returned from a select query, mysqli_fetch_array() to fetch row arrays from query results, and mysqli_close() to close an open database connection. Each function has a defined syntax using parameters like the database connection handler and query string.