Inspired by the hit computer series from the 1990s, Catz has players adopting digital versions of 13 different breeds including a Persian, Himalayan, Abyssinian, and Ocicat from an in-game pet store before naming and then caring for their animal in and around a house. As in most games in the genre, players must monitor a number of traits to help care for their pet as well as develop a feeding schedule and make time to play with or groom the animal.

Achieving high rankings in categories such as affection, health, and energy will not only ensure a cat's long life, but also increase the number of available toys, supplies, and other items for players to use. Each cat can also be immortalized in a hall of fame after being retired, and different breed variants will gradually open up as players become more proficient in raising their pet. Curious Catz owners can explore each other's neighborhoods through a wireless network.