Core-collapse supernovae (CCSNe) are the powerful explosions of massive stars that occur when they exhaust their nuclear fuel. They play a crucial role in the evolution of the Universe, producing most elements heavier than iron and leading to the formation of neutron stars and black holes. Matter in CCSNe exists at extremely large densities and CCSNe are often viewed as cosmic laboratories for nuclear and neutrino physics. Despite their importance to our understanding of many aspects of the Universe, the details of how they explode are still unclear. In this talk, I will review the recent progress in modeling CCSN explosions, with an emphasis on our recent simulations. I will also discuss how their gravitational wave and neutrino signature may reveal important information about the explosion mechanism and their progenitors.