Extragalactic science with the next generation of ground based TeV γ-ray telescopes

The ground based Cherenkov telescope experiments H.E.S.S., MAGIC, and VERITAS, and the space borne Fermi Gamma-Ray Space Telescope are currently exploring the galactic and extragalactic Universe in γ-rays. At the time of writing this article, a large number of Active Galactic Nuclei have been studied in great detail and the γ-ray observations have had a major impact on our understanding of the structure of jets from these objects. In this contribution, the status of ground based γ- ray observations of AGN and other extragalactic source classes is reviewed as of October, 2008. After discussing source classes that could be detected with next generation ground based experiments like AGIS, CTA, and HAWC, the potential impact of the observations on the fields of high energy astrophysics, structure formation, observational cosmology, and fundamental physics is reviewed. We close with a discussion of the technical requirements that arise from the science drivers.