  Few years ago, Boltzmann neutrino transport led to a new and reliable
generation of spherically symmetric models of stellar core collapse and
postbounce evolution. After the failure to prove the principles of the
supernova explosion mechanism, these sophisticated models continue to
illuminate the close interaction between high-density matter under extreme
conditions and the transport of leptons and energy in general relativistically
curved space-time. We emphasize that very different input physics is likely to
be relevant for the different evolutionary phases, e.g. nuclear structure for
weak rates in collapse, the equation of state of bulk nuclear matter during
bounce, multidimensional plasma dynamics in the postbounce evolution, and
neutrino cross sections in the explosive nucleosynthesis. We illustrate the
complexity of the dynamics using preliminary 3D MHD high-resolution simulations
based on parameterized deleptonization. With established spherically symmetric
models we show that typical features of the different phases are reflected in
the predicted neutrino signal and that a consistent neutrino flux leads to
electron fractions larger than 0.5 in neutrino-driven supernova ejecta.
