Neutrinos are considered to be one of the most important ingredients of collapse-driven supernovae. In the last couple of years, we have seen major progress in both numerical modelling and microphysical understanding of supernova neutrinos. The successful explosion, however, is still elusive. In the former half of this article, we give a brief overview on the current status of the theoretical understanding of the supernova mechanism. In the latter half, we present some new results on multi-dimensional aspects such as rapid rotations, strong magnetic fields and resultant anisotropic neutrino heating, to which our group is currently paying particular attention as an important element for successful explosions. We employ both statical and dynamical approaches. The gravitational waves obtained in the dynamical computations are summarized in an appendix.
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