In this paper, we summarize some of the new ideas concerning supernova neut
rinos and their angular, spatial, and energy distributions in protoneutron
stars. Furthermore, we touch on some of the recent speculations concerning
the systematics with progenitor mass of core-collapse supernova explosion e
nergies and Ni-56 yields. In addition, we discuss some of the prominent fea
tures predicted in galactic neutrino bursts, features that would be detecte
d by underground neutrino telescopes now on line. Recently, a few theoretic
al teams have started to explore afresh neutrino-matter interactions and hi
gh-precision algorithms for determining the neutrino radiation fields. We p
resent some preliminary results from one of those teams.