In the light of recent significant progress on both the observational and t
heoretical fronts, we review the status of white dwarf stars as cosmochrono
meters. These objects represent the end products of stellar evolution for t
he vast majority of stars and, as such, can be used to constrain the ages o
f various populations of evolved stars in the Galaxy. For example, the olde
st white dwarfs in the solar neighborhood (the remnants of the very first g
eneration of intermediate-mass stars in the Galactic disk) are still visibl
e and can be used, in conjunction with cooling theory, to estimate the age
of the disk. More recent observations suggest the tantalizing possibility t
hat 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 t
he 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 wh
ite dwarf populations should be routinely discovered and studied in open an
d globular clusters.