The visible world made of stars, planets and interstellar gas makes up only 5% of the energy content of the universe. About 70% is made of an ill-understood form of energy called dark energy and 25% is a mysterious form of mass called dark matter. It has no detectable interactions with light, and through gravitational interactions gives the universe its current looks on the largest distance scales. But its microscopic identity is unknown, unlike the visible world that is explained by the Standard Model of particle physics. Therefore dark matter is one of the foremost scientific mysteries of our times. Since very little is known about its microscopic properties, its possible identities appear endless. This is best encapsulated in the more than 90 orders of magnitude that dark matter masses could span, from 10^-24 eV to 10^8 solar masses. Over this range of masses dark matter may be described as a wave or field, a particle, a macroscopic object, or halo substructure, which includes black holes and topological defects. A promising strategy to confront such remarkable diversity in scenarios is to exploit physical systems with remarkable diversity in characteristics. Stars, and in particular compacts stars such as white dwarfs and neutron stars, provide such a system. Our understanding of compact stars has been enhanced at the intersection of many branches of physics: astrophysics, general relativity, particle physics, nuclear physics, statistical physics, thermodynamics, and plasma physics. It is no surprise that they feature in numerous tests of fundamental physics, and it should come as no surprise that they are also ideal laboratories to search for dark matter. They have several striking properties: very high densities, with accompanying steep gravitational potentials, sometimes deeply degenerate constituent fermions, often very low temperatures, the presence of nucleon superfluidity, ultra-strong magnetic fields, extreme regularity in rotation rivalling the precision of atomic clocks, and powerful gravitational radiation emitted during binary mergers, to name a few. My proposed work will make use of these unique properties of compact stars to hunt for the secret identity of dark matter.