AbstractIn this paper I summarize some of the recent advances in studies of dense matter. Research on phase separation in the binary ionic mixtures (BIMs) that constitute the matter in white dwarfs has been motivated by the need to obtain accurate estimates for the ages of the faintest white dwarfs and thus of the disk of our Galaxy. Substantial age increases appear possible, but it is not yet clear whether such large increases occur in real white dwarfs. A second advance is the prediction,

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... d on state-of-the-art physical calculations, that ionization of H at low temperatures and increasing densities may occur via a first-order "plasma phase transition" (PPT). Astrophysical consequences of this result are still being explored in an effort to test this prediction. Related to these equation-of-state calculations are calculations of the enhancement of nuclear reaction rates at high densities. New thermonuclear rates have been computed for C+C reactions in BIMs, although there is currently some controversy about results at the highest densities. New pycnonuclear reaction rates have also been calculated for BIMs, and it has been suggested that He-burning atT= 0 may occur through a first-order phase transition. Finally, calculations of the equation of state of matter in strong magnetic fields and of radiative opacities at high densities have undergone very recent and substantial improvements, which are just beginning to be utilized in astrophysical calculations.