Most Tetris games made since 2001 let you twist blocks into gaps that seem impossible. Some of these setups can be used to help correct mistakes, and others are just for fun. Even if you only learn the T-Spins, you’ll be able to send garbage faster than just back-to-back Tetrises all day. If you want to play around with twists, try King of Stackers, a turn-based Tetris battle sim where you can use every trick in the book to make the most of your seven pieces per turn.
Source: Chopin's Twist Guide – YouTube