The extragalactic gamma-ray sky at TeV energies is dominated by blazars, a subclass of accreting super-massive black holes with powerful relativistic outflows directed at us. Only constituting a small fraction of the total power output of black holes, blazars were thought to have a minor impact on the universe at best. As we argue here, the opposite is true and the gamma-ray emission from TeV blazars can be thermalized via beam-plasma instabilities on cosmological scales with order unity efficiency, resulting in a potentially dramatic heating of the low-density intergalactic medium. Here, we review this novel heating mechanism and explore the consequences for the formation of structure in the universe. In particular, we show how it produces an inverted temperature-density relation of the intergalactic medium that is in agreement with observations of the Lyman-alpha forest. This suggests that blazar heating can potentially explain the paucity of dwarf galaxies in galactic halos and voids, and the bimodality of galaxy clusters. This also transforms our understanding of the evolution of blazars, their contribution to the extra-galactic gamma-ray background, and how their individual spectra can be used in constraining intergalactic magnetic fields.
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