Twists let a player fix some otherwise difficult situations. These examples cover recent games, but may not work for earlier Tetris games.
Twists with T (or T-Spin)
A well-known twist involves the tetromino T.
Other variants exist.
Some may not seem possible, but the game will allow them regardlessly.
Twists with I
If changing position to the second row, rotate three times so to twist on lower-middle square.
If changing positions to the right columns, turn right. If left, turn left.
Twists with S and Z
If using S, rotate right. If using Z, rotate left.
In this case, if using S, turn left and if using Z, turn right.
Twists with J and L