  The most powerful persistent accelerators in the Universe are jetted active
galaxies. Blazars, galaxies whose jets are directed towards Earth, dominate the
extragalactic gamma-ray sky. Still, most of the highest-energy particle
accelerators likely elude detection. These extreme blazars, whose radiated
energy can peak beyond 10 TeV, are ideal targets to study particle acceleration
and radiative processes, and may provide links to cosmic rays and astrophysical
neutrinos. The growing number of extreme blazars observed at TeV energies has
been critical for the emergence of gamma-ray cosmology, including measurements
of the extragalactic background light, tight bounds on the intergalactic
magnetic field, and constraints on exotic physics at energies inaccessible with
human-made accelerators. Tremendous progress has been achieved over the past
decade, which bodes well for the future, particularly with the deployment of
the Cherenkov Telescope Array.
