  The explosion of core-collapse supernova depends on a sequence of events
taking place in less than a second in a region of a few hundred kilometers at
the center of a supergiant star, after the stellar core approaches the
Chandrasekhar mass and collapses into a proto-neutron star, and before a shock
wave is launched across the stellar envelope. Theoretical efforts to understand
stellar death focus on the mechanism which transforms the collapse into an
explosion. Progress in understanding this mechanism is reviewed with particular
attention to its asymmetric character. We highlight a series of successful
studies connecting observations of supernova remnants and pulsars properties to
the theory of core-collapse using numerical simulations. The encouraging
results from first principles models in axisymmetric simulations is tempered by
new puzzles in 3D. The diversity of explosion paths and the dependence on the
pre-collapse stellar structure is stressed, as well as the need to gain a
better understanding of hydrodynamical and MHD instabilities such as SASI and
neutrino-driven convection. The shallow water analogy of shock dynamics is
presented as a comparative system where buoyancy effects are absent. This
dynamical system can be studied numerically and also experimentally with a
water fountain. The potential of this complementary research tool for supernova
theory is analyzed. We also review its potential for public outreach in science
museums.
