Stars have the potential to be excellent dark matter detectors; dark matter could heat them up, destroy them by forming black holes, or modify heat transport. To predict when and how this might happen, we need to compute the scattering rate of dark matter inside stars. In this talk, I will describe how, for a wide range of dark matter models, this requires taking into account collective effects - that is, coherent scattering with many particles inside the star. These effects have been neglected in many previous treatments; I will show how they can enhance or suppress naive predictions for dark matter scattering rates by orders of magnitude. Calculations can be performed systematically by computing in-medium effective propagators, using the apparatus of thermal field theory.