  We present new white dwarf cooling models which incorporate an accurate outer
boundary condition based on new opacity and detailed radiative transfer
calculations. We find that helium atmosphere dwarfs cool considerably faster
than has previously been claimed, while old hydrogen atmosphere dwarfs will
deviate significantly from black body appearance. We use our new models to
derive age limits for the Galactic disk. We find that the Liebert, Dahn & Monet
(1988) luminosity function yields an age of only 6 Gyr if it is complete to
stated limits. However, age estimates of individual dwarfs and the luminosity
function of Oswalt et al (1995) are both consistent with disk ages as large as
\sim 11 Gyr. We have also used our models to place constraints on white dwarf
dark matter in Galactic halos. We find that previous attempts using inadequate
cooling models were too severe and that direct detection limits allow a halo
that is 11 Gyr old. If the halo is composed solely of helium atmosphere dwarfs,
the lower age limit is only 7.5 Gyr. We also demonstrate the importance of
studying the cooling sequences of white dwarfs in Globular clusters.
