  The nature of the dark matter in the haloes of galaxies is one of the
outstanding questions in astrophysics. All stellar candidates, until recently
thought to be likely baryonic contributions to the Halo of our Galaxy, are
shown to be ruled out. Faint stars and brown dwarfs are found to constitute
only a few percent of the mass of the Galaxy. Stellar remnants, including white
dwarfs and neutron stars, are shown to be very constrained as well. High energy
gamma-rays observed in HEGRA data place the strongest constraints, $\Omega_{WD}
< 3 \times 10^{-3} h^{-1}$, where $h$ is the Hubble constant in units of 100 km
s$^{-1}$ Mpc$^{-1}$. Hence one is left with several unanswered questions: 1)
What are MACHOs seen in microlensing surveys? 2) What is the dark matter in our
Galaxy? Indeed a nonbaryonic component in the Halo seems to be required.
