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 .