In the light of recent significant progress on both the observational and theoretical fronts, we review the status of white dwarf stars as cosmochronometers. These objects represent the end products of stellar evolution for the vast majority of stars and, as such, can be used to constrain the ages of various populations of evolved stars in the Galaxy. For example, the oldest white dwarfs in the solar neighborhood (the remnants of the very first generation of intermediate-mass stars in the Galactic disk) are still visible and can be used, in conjunction with cooling theory, to estimate the age of the disk. More recent observations suggest the tantalizing possibility that a population of very old white dwarfs inhabits the Galactic halo. Such a population may contribute significantly to baryonic "dark" matter in the Milky Way and may be used to obtain an independent estimate of the age of the halo. In addition, white dwarf cosmochronology is likely to play a very significant role in the coming era of giant 8-10 m telescopes when faint white dwarf populations should be routinely discovered and studied in open and globular clusters.