The show concentrates on Oggy, an anthropomorphic blue cat, who want to spend his days contentedly watching television and eating - or else for the three roaches in the household: Joey, Dee Dee and Marky (named after members of the punk group Ramones). The trio usually enjoy making Oggy's life miserable, that involves mischief ranging from (generally) plundering his refrigerator to such awkward things such as hijacking the train Oggy just boarded. Oggy usually finds creatures accompanying him to the end of the episode, like crabs, clams, a horse, an incredibly technologically advanced child, a puppy, with an octopus. However, it isn't really always Oggy who wins.
The cartoon relies on slapstick humour, much like its "ancestor", Tom and Jerry, only amplifying the level of extremities up a notch. While traditional slapstick cartoon characters prefer dropping anvils and pianos on each other, this show sometimes uses buses or submarines. Despite these, however, most gags are typically accessible and enjoyable for younger viewers. Since dialogue is kept low, the humour is entirely visual.