Abstract The nature of the dark matter in the Halo of our Galaxy remains a mystery. Arguments are presented that the dark matter does not consist of ordinary stellar or substellar objects, i.e., the dark matter is not made of faint stars, brown dwarfs, white dwarfs, or neutron stars. In fact, faint stars and brown dwarfs constitute no more than a few percent of the mass of our Galaxy, and stellar remnants must satisfy Ω WD ≤3×10 −3h −1 , where h is the Hubble constant in units of 100 km s −1 Mpc −1 . On theoretical grounds one is then pushed to more exotic explanations. Indeed a nonbaryonic component in the Halo seems to be required.