  The nature of the dark matter in the Universe is one of the outstanding
questions in astrophysics. In this talk, I address possible stellar baryonic
contributions to the 50-90% of our Galaxy that is made of unknown dark matter.
First I show that faint stars and brown dwarfs constitute only a few percent of
the mass of the Galaxy. Next, I show that stellar remnants, including white
dwarfs and neutron stars, are also insufficient in abundance to explain all the
dark matter of the Galaxy. High energy gamma-rays observed in HEGRA data place
the most robust constraints, $\Omega_{WD} < 3 \times 10^{-3} h^{-1}$, where $h$
is the Hubble constant in units of 100 km s$^{-1}$ Mpc$^{-1}$. Overproduction
of chemical abundances (carbon, nitrogen, and helium) provide the most
stringent constraints, $\Omega_{WD} < 2 \times 10^{-4} h^{-1}$. Comparison with
recent updates of microlensing data are also made. According to the gamma-ray
limit, all Massive Compact Halo Objects seen by the experiments (Machos) can be
white dwarfs if one takes the extreme numbers; however, from chemical
overproduction limits, NOT all Machos can be white dwarfs. Comments on recent
observations of the infrared background and of white dwarfs are also made. In
conclusion, a nonbaryonic component in the Halo seems to be required.
