Heavy dark matter coupled to much lighter force carriers exhibits a range of interesting behaviors that are not well-characterized by the usual perturbative Feynman diagram expansion, including long-range interactions, annihilation rates modified by both large velocity-dependent enhancements and large logarithms, and the presence of bound states. There has been great interest in recent years in dark sectors containing both dark matter and much lighter particles; as the LHC continues to constrain low-scale supersymmetry, even classic weakly interacting dark matter candidates may need to be heavy relative to the weak gauge bosons. I will describe recent work to characterize the novel properties of heavy dark matter coupled to light force carriers, in two principal directions: (1) the precision calculation of heavy wino dark matter annihilation to line photons using effective field theory, now to NLL’ order, and (2) the properties of dark-sector bound states where multiple force carriers and several states in a dark matter multiplet may be involved, using the wino as an example. I will discuss the importance of these results for indirect detection experiments searching for the products of dark matter annihilation.