[en] A nascent neutron star resulting from stellar collapse is a prodigious source of neutrinos of all flavors. While the most basic features of this neutrino emission can be estimated from simple considerations, the detailed simulation of the neutrinos' decoupling from the hot neutron star is not yet computationally tractable in its full glory, being a time-dependent six-dimensional transport problem. Nevertheless, supernova neutrino fluxes are of great interest in connection with the core-collapse supernova explosion mechanism and supernova nucleosynthesis, and as a potential probe of the supernova environment and of some of the neutrino mixing parameters that remain unknown; hence, a variety of approximate transport schemes have been used to obtain results with reduced dimensionality. However, none of these approximate schemes have addressed a recent challenge to the conventional wisdom that neutrino flavor mixing cannot impact the explosion mechanism or r-process nucleosynthesis