We discuss the capture of dark matter in white dwarfs (WD), the most abundant stellar remnants, as complementary to terrestrial searches. We consider the capture of DM due to interactions with either ion or the degenerate electron component of WDs. We account for the stellar structure, star opacity, realistic nuclear form factors, and temperature effects to discuss the capture rate. In the case of ions we use a Maxwell Boltzmann distribution while for the degenerated electrons, we require a formalism that properly incorporates Pauli blocking and a relativistic treatment for electrons. We also discuss the dark matter evaporation rate. The DM interactions can be constrained by comparing the heating rate, due to the presence of DM in the star nucleus, with observations of cold WDs. We have calculated the capture rate and applied this technique to observed WDs in the Messier 4 (M4) globular cluster to set bound on DM interactions.