The physics of propagating TeV gamma-rays: from plasma instabilities to cosmological structure formation 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 I will 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, substantially modifying the thermal history of the intergalactic medium, the statistics of the Lyman-alpha forest, and suppressing late formation of dwarf galaxies in cosmological voids. I will review the plasma physics of this novel mechanism and highlight the successes and open questions. If these can be solved, 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. Contributors: C. Pfrommer, HITS Heidelberg, christoph.pfrommer@h-its.org A. Broderick, Perimeter Institute/Waterloo University, abroderick@perimeterinstitute.ca P. Chang, University of Wisconsin-Milwaukee, chang65@uwm.edu E. Puchwein, University of Cambridge, puchwein@ast.cam.ac.uk M. Shalaby, Perimeter Institute/Waterloo University, mshalaby@perimeterinstitute.ca A. Lamberts, Caltech, lamberts@caltech.edu