  We review the status of the current quest to understand the mechanism of
core-collapse supernovae, if neutrino-driven. In the process, we discuss the
spherical explosion paradigm and its problems, some results from our new suite
of collapse calculations performed using a recently-developed 1D implicit,
multi-group, Feautrier/tangent-ray, Boltzmann solver coupled to explicit
predictor/corrector hydrodynamics, the basic energetics of supernova
explosions, and the promise of multi-D radiation/hydro simulations to explain
why the cores of massive stars explode.
