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.
After (or rather before) the nightmares, Vincent hangs out at the Stray Sheep. In this bar, he can send and receive text messages, drink, talk to people or play an arcade game called Rapunzel (a series of 8-bit-like short climbing levels) until he goes back to sleep. When Vincent has to make choices, a blue and red gauge appears. This gauge indicates whether Vincent is more inclined towards law or chaos, which will influence the game's ending. Apart from the story mode, there is Babel, a special challenge in which one or two players have to climb as high as they can to achieve new records. Babel must first be unlocked by meeting certain conditions in story mode.