Cockroaches are generalized insects with few special adaptations, and may be among the most primitive living Neopteran insects. They have a relatively small head and a broad, flattened body, and most species are reddish-brown to dark brown. They have large compound eyes, two ocelli, and long, flexible antennae.Cockroaches have been around since the time of dinosaurs! A cockroach can live almost a month without food. A cockroach can live about two weeks without water.