  The explosion mechanism of core-collapse supernovae is a long-standing
problem in stellar astrophysics. We briefly outline the main contenders for a
solution and review recent efforts to model core-collapse supernova explosions
by means of multi-dimensional simulations. We discuss several suggestions for
solving the problem of missing or delayed neutrino-driven explosions in
three-dimensional supernova models, including -- among others -- variations in
the microphysics and large seed perturbations in convective burning shells.
Focusing on the neutrino-driven mechanism, we summarise currents efforts to
predict supernova explosion and remnant properties based on first-principle
models and on more phenomenological approaches.
