The interaction between two stars in a binary system can lead to the dynamically stable accretion of H- or He-rich matter onto a degenerate white dwarf (WD). The accreted material constitutes a fresh thermonuclear fuel source that, when ignited, yields a wide variety of observable consequences. In this dissertation, we utilize a combination of analytic, semi-analytic, and numeric computations to explore the physics of stably-burning supersoft x-ray sources, classical and recurrent novae, including novae in cataclysmic variables with He core WDs, and convective He-burning shells. We also present the first detailed calculations of light curves and spectra for a newly predicted class of faint thermonuclear supernovae powered by He detonations. |