The Universe is largely transparent to γ -rays in the GeV energy range, making these high-energy photons valuable for exploring energetic processes in the cosmos. After 7 years of operation, the Fermi   Gamma-ray Space Telescope has produced a wealth of information about the high-energy sky. This review focuses on extragalactic γ -ray sources: what has been learned about the sources themselves and about how they can be used as cosmological probes. Active galactic nuclei (blazars, radio galaxies, Seyfert galaxies) and star-forming galaxies populate the extragalactic high-energy sky. Fermi observations have demonstrated that these powerful non-thermal sources display substantial diversity in energy spectra and temporal behavior. Coupled with contemporaneous multifrequency observations, the Fermi results are enabling detailed, time-dependent modeling of the energetic particle acceleration and interaction processes that produce the γ -rays, as well as providing indirect measurements of the extragalactic background light and intergalactic magnetic fields. Population studies of the γ -ray source classes compared to the extragalactic γ -ray background place constraints on some models of dark matter. Ongoing searches for the nature of the large number of γ -ray sources without obvious counterparts at other wavelengths remain an important challenge.