  Massive stars (M> 10Msun) end their lives with spectacular explosions due to
gravitational collapse. The collapse turns the stars into compact objects such
as neutron stars and black holes with the ejection of cosmic rays and heavy
elements. Despite the importance of these astrophysical events, the mechanism
of supernova explosions has been an unsolved issue in astrophysics. This is
because clarification of the supernova dynamics requires the full knowledge of
nuclear and neutrino physics at extreme conditions, and large-scale numerical
simulations of neutrino radiation hydrodynamics in multi-dimensions. This
article is a brief overview of the understanding (with difficulty) of the
supernova mechanism through the recent advance of numerical modeling at
supercomputing facilities. Numerical studies with the progress of nuclear
physics are applied to follow the evolution of compact objects with neutrino
emissions in order to reveal the birth of pulsars/black holes from the massive
stars.
