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 nonthermal 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.