  White dwarfs and neutron stars are far-reaching and multi-faceted
laboratories in the hunt for dark matter. We review detection prospects of
wave-like, particulate, macroscopic and black hole dark matter that make use of
several exceptional properties of compact stars, such as ultra-high densities,
deep fermion degeneracies, low temperatures, nucleon superfluidity, strong
magnetic fields, high rotational regularity, and significant gravitational wave
emissivity. Foundational topics first made explicit in this document include
the effect of the ``propellor phase" on neutron star baryonic accretion, and
the contribution of Auger and Cooper pair breaking effects to neutron star
heating by dark matter capture.
