Catherine follows the story of Vincent Brooks, who is caught between his girlfriend Katherine McBride, who may be pregnant, and Catherine, a 22 year-old blonde he met at the Stray Sheep, a bar he hangs out at. Since his encounter with Catherine, Vincent has been having nightmares every night. The nightmares are puzzle-platforming sections shaped as tower-like levels in which Vincent must climb to the top by pulling and pushing blocks. While he climbs, the level falls apart, and sheep characters try to shove him back down. Along the way, the player can learn various climbing strategies to adapt to different situations. In some levels, a giant boss tries killing Vincent with a multitude of attacks.