  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: 1) to
focus attention on the interesting problems whose resolution will bring needed
progress, and 2) to assess the current status of the theoretical art.
