  Two-dimensional hydrodynamic simulations of stellar core-collapse with and
without rotation are presented which for the first time were performed by
solving the Boltzmann equation for the neutrino transport including a
state-of-the-art description of neutrino interactions. Although convection
develops below the neutrinosphere and in the neutrino-heated region behind the
supernova shock, the models do not explode. This suggests missing physics,
possibly with respect to the nuclear equation of state and weak interactions in
the subnuclear regime. However, it might also indicate a fundamental problem of
the neutrino-driven explosion mechanism.
