We report here on recent progress in understanding the birth conditions of neutron stars and the way how supernovae explode. More sophisticated numerical models have led to the discovery of new phenomena in the supernova core, for example a generic hydrodynamic instability of the stagnant supernova shock against low-mode nonradial deformation and the excitation of gravity-wave activity in the surface and core of the nascent neutron star. Both can have supportive or decisive influence on the inauguration of the explosion, the former by improving the conditions for energy deposition by neutrino heating in the postshock gas, the latter by supplying the developing blast with a flux of acoustic power that adds to the energy transfer by neutrinos. While recent two-dimensional models suggest that the neutrino-driven mechanism may be viable for stars from about 8 solar masses to at least 15 solar masses, acoustic energy input has been advocated as an alternative if neutrino heating fails. Magnetohydrodynamic effects constitute another way to trigger explosions in connection with the collapse of sufficiently rapidly rotating stellar cores, perhaps linked to the birth of magnetars. The global explosion asymmetries seen in the recent simulations offer an explanation of even the highest measured kick velocities of young neutron stars.
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