Extragalactic γ-ray astronomy is in its infancy. In this paper a review is presented of the γ-ray emission of the few individual objects observed to date and some conclusions are drawn as to their possible general characteristics. A number of scenarios suitable for the generation of γ-rays are presented in the light of these recent measurements. The contribution of active galactic nuclei to the cosmic diffuse γ-ray background is estimated and the implications discussed. It is evident that future extragalactic γ-ray observational programs with instruments having improved sensitivity are required. Some objectives of such missions are outlined.