One can frame a game or a puzzle as a decision problem: from this configuration, does the puzzle have a solution? Can Black win the game? The computational complexity of the decision problem can then be investigated. I will begin by reviewing the properties of the complexity classes I'll be discussing (NP-complete, PSPACE-complete, etc.), then briefly present several recent hardness results, including sliding-block puzzles, sliding-coin puzzles, TipOver, Rush Hour, Sokoban, hinged polygon dissections, plank puzzles, the Dyson telescope game, Amazons, and Konane.