The show centers on Oggy, a content and lazy, albeit very tender fat blue cat, who would usually spend his days watching TV and cooking - if it wasn't 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 generally 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.
The cartoon itself 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 even buses or submarines. Despite these however, most gags are easily accessible and enjoyable for younger viewers. Since dialog is kept to a minimum the humour is entirely visual.