Towards a synthesis of core-collapse supernova theory

New insights into the mechanism and character of core-collapse supernova explosions are transforming the approach of theorists to their subject. The universal realization that the direct hydrodynamic mechanism does not work and that a variety of hydrodynamic instabilities can influence the viability of theoretical explosions has ushered in a new era in supernova modeling. In this paper, I discuss the important physical and technical issues that remain. I review the neutrino-driven mechanism, the possible roles of Rayleigh-Taylor instabilities, questions in neutrino transport, and the various observational constraints within which theorists must operate. However, a consensus has yet to be achieved among active workers concerning many important details and some essential phenomenology. This synopsis is meant to accomplish two things: (i) to focus attention on the interesting problems whose resolution will bring needed progress, and (ii) to assess the current status of the theoretical art.