  We summarize recent improvements in model atmosphere and internal structure
of faint white dwarfs. We derive an analytical cooling theory which illustrates
the effects of various physical processes on the energy budget and the cooling
history of cool white dwarfs. We consider in particular the effect of chemical
fractionation at crystallization. This process, although it liberates a small
amount of energy, affects significantly the cooling time of white dwarfs at
their low-luminosity stages. This modifies the age of the faintest white dwarf
ever observed, ESO 439-26, and bears important consequences for the Galactic
implications of white dwarf evolution, age of the Galactic disk and expected
contribution to the halo mass.
  We briefly consider the remaining major uncertainties in white dwarf cooling
theory.
