The show centers on Oggy, a content, blue cat, who would prefer to spend his days watching television and eating - if not for the three roaches in the household: Joey, Dee Dee and Marky (named after members of the punk group Ramones). The trio seems to enjoy making Oggy's life miserable, which involves mischief ranging from (in most cases) plundering his fridge to such awkward things like hijacking the train Oggy just boarded. Oggy usually finds creatures accompanying him to the end of the episode, such as crabs, clams, a horse, a very technologically advanced child, a puppy, and an octopus. However, it's not always Oggy who wins.

By all appearances, Dexter is your typical boy. Your typical pointy-boot wearing, lab-coat sporting, European-sounding three-foot-tall boy. But when it comes to science, he is a genius. Dexter's biggest challenge, however, is keeping his meddling sister Dee Dee from interfering with his next great invention.