Database languages allow developers to define, access, and manipulate data stored in databases. There are four main categories of database languages: data definition languages (DDL) are used to define database structure; data manipulation languages (DML) are used to insert, update, and retrieve data; data control languages (DCL) control user access and privileges; and transaction control languages (TCL) group statements into logical transactions and allow committing or rolling back changes. Common statements include CREATE, SELECT, INSERT, UPDATE, DELETE, COMMIT, and ROLLBACK.