The thermal properties and neutrino emissivity of matter in the dense, degenerate cores of white dwarfs, together with efficient heat transport through the high-density envelopes of these stars, affect the theoretical white dwarf luminosity function. The most recent observational data show departures from the results of elementary cooling theory at both high and low luminosities. Extreme UV and soft x-ray observations from space show the necessity of neutrino cooling for white dwarfs, have begun to provide some clues to the nature of their progenitors, and may be revealing evidence for white dwarf coronae. Investigations of very cool white dwarfs appear to show a luminosity cutoff due to the finite age of the galactic disk and have revealed very high density stellar atmospheres with quite remarkable physical properties. Element abundances in white dwarf atmospheres are beginning to be understood on the basis of accretion, convection, and diffusion theory, but the presence of C and the absence of H in some white dwarf spectra remain out standing problems. Investigations of non-radial oscillations in white dwarfs may soon provide a sensitive probe of the chemical stratification and material properties in these stars. White dwarf stars are also essential components of cataclysmic binaries, and a few recent results concerning these systems are briefly reviewed.