Twists with J and L

Notes:
 * CW - Clockwise
 * CCW - Counter-clockwise
 * † - Prior to soft dropping or firm dropping
 * †† - Mirror diagram and directions for L tetromino

General
Works in virtually all versions, including Tetris (Game Boy) and Atari Rotation:

Works with TGM and SRS:

(For this one, the block highlighted in red is needed in TGM, but is optional in SRS. The edge of the field may also be used in place of that block.)