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The production of dark matter via thermal decoupling from the primordial plasma, and the direct, indirect and collider signals associated with this mechanism, have been the pillars of dark matter phenomenology in the past decades. In sharp contrast to the sub-TeV regime, the interactions of thermal-relic dark matter with multi-TeV or larger mass manifest as long-range. This is supported by unitarity arguments, and shown by explicit calculations in WIMP and other models. The long-range nature of the interactions gives rise to non-perturbative effects, with the most prominent being the existence of bound states. The formation and decay of unstable bound states in the early universe decrease the dark matter density, thereby changing its predicted mass and/or couplings. This can have severe implications for all experimental probes, particularly for collider and indirect searches.