  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.
