The show centers on Oggy, an anthropomorphic blue cat, who would want to spend his days contentedly watching tv and eating - otherwise 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 (typically) plundering his refrigerator to such awkward such things as hijacking the train Oggy just boarded. Oggy usually finds creatures accompanying him on the end from the episode, like crabs, clams, a horse, a very technologically advanced child, a puppy, plus an octopus. However, it is not always Oggy who wins.
The cartoon relies upon slapstick humour, much like its "ancestor", Tom and Jerry, only amplifying the amount of extremities up a notch. While traditional slapstick cartoon characters prefer dropping anvils and pianos on every other, this show sometimes uses buses or submarines. Despite these, however, most gags are often accessible and enjoyable for younger viewers. Since dialogue is kept as small as possible, the humour is entirely visual.