Observed spectra of supernovae allow the empirical classification of supernovae into two basic categories, Type I with little or no evidence of hydrogen, and Type II with obvious evidence for hydrogen. The broad class of Type I can be subdivided depending on whether helium or silicon and other intermediate mass elements is observed. Understanding the physical processes that underlie these classifications---the progenitor evolution. the explosion mechanism, and end products---requires calculation of radiative transfer and model spectra. While most Type II occur in evolved massive stars that undergo core collapse. some may span the dividing line between degenerate and non-degenerate carbon burning and involve both core collapse and thermonuclear explosion. Type Ia are still most plausibly explained as thermonuclear explosions in carbon/oxygen white dwarfs in binary systems. Type Ib reveal helium atmospheres and are probably the result of core collapse in the helium core of a massive star that has lost its hydrogen envelope to a binary companion or to a wind. Type Ic supernovae are probably related to Type Ib but have also lost their helium envelope to reveal a mantle rich in oxygen.

At intermediate mass transfer rates, accretion disks in binary star systems undergo a thermally-driven limit cycle instability. This instability leads to outburst episodes when the disk is bright and the flow through the disk is rapid separated by long intervals when the disk is dim and the flow through it is low. This intrinsic outburst mechanism can help to understand a wide range of astrophysical phenomena from dwarf novae to soft X -ray transients involving white dwarf, neutron star, and black holes. and to a deeper understanding of the mechanism of angular transport and viscosity in the accretion disk.