Classical: Longest format for deep strategy.
Rapid: Faster than Classical, slower than Blitz.
Blitz: Very fast; only a few minutes for the full game.
Bullet: Ultra-fast (often ≤3 minutes per player).

Chess960 (Fischer Random): Back‑rank pieces randomized to reduce opening theory.
Crazyhouse: Captured pieces change color and can be dropped back on the board.
Three‑check (3‑Check): Win by giving three checks to the king.
Bughouse (Doubles): 2v2; captured pieces are passed to your partner to drop in.
King of the Hill: Win by bringing your king to a central square (d4, e4, d5, e5).
Atomic: Captures explode surrounding pieces; explode the opponent’s king to win.
Horde: One side is a pawn horde vs. a normal army.
Infinite Chess: Played on an unbounded board with special rules/analyses.

Xiangqi: Chinese chess with a river and cannons.
Shogi: Japanese chess where captured pieces can be dropped back in.
Checkers (Draughts): Capture‑focused cousin; diagonal moves and jumps.