When stars run out of nuclear fuel, gravity takes over and forces the star to contract. If the final mass of the star is less than 1.4 times the mass of the sun, the contraction will stop when the star becomes a white dwarf star. These stars are tiny balls, packing the mass of the sun into spheres the size of the earth. This talk will review our understanding of the rather unusual properties of these stars, whose surface chemical compositions are unlike those of any other stars. Recent research has at last provided good observational support to the theory of stellar degeneracy, a Nobel-Prize winning theory which is the basis for the discovery of black holes. I will briefly review the current status of our search for black holes.