In this paper, I summarize two new developments in the theory of core-collapse supernovae. The first is the recent establishment of an analytic context for understanding neutrino-driven explosions. Converting the supernova problem into an eigenvalue problem, Burrows & Goshy (1993) have derived a critical condition on neutrino luminosity and mass accretion rate through a stalled bounce shock for instability and explosion. The second development is the recent calculation of Burrows & Fryxell (1993) of the boost in the neutrino luminosities by the Rayleigh-Taylor-like overturn of the shocked mantle of a protoneutron star. This boost may turn duds into explosions and may be the missing ingredient of supernova theory.
Core-collapse supernova predominate in the supernova bestiary (van den Bergh & Tammann 1991), but have challenged theorists during the entire post-war era of astrophysics. The sparseness of data that directly probe the dynamics of collapse and shock generation has hobbled advances in supernova theory, as has the wider than normal range of physical inputs required from the gravitational, neutrino, hydrodynamic, transport, thermodynamic, and nuclear realms. Extracting the essential elements of the explosion mechanism has not been easy. As a result, supernova theory has been perceived at various times to be confusing, arcane, hopeless, muddled, or vulnerable to the quick fix by a well-meaning Cincinnatus.