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 x 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 x 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.