In this paper, I summarise the recent results of our study on the core-collapse supernova and related phenomena. Among the issues addressed are (1) long-term ID simulations of core-collapse supernovae, (2) global asymmetry of supernova, and (3) collapse of more massive stars and neutrino signals. In the first topic, I report our latest 1D simulations for more than a second after the bounce and demonstrate that the difference of EOS's manifests itself more clearly in the later phase of the core collapse. In the second part, I discuss hydrodynamic instabilities as a possible cause for the global asymmetry that may be a generic feature of core-collapse supernova. The mode analysis of the non-spherical instability of the standing accretion shock is presented. Inelastic scatterings of neutrino on nuclei are also discussed in this context. Finally, I mention the gravitational collapse of more massive stars which will produce not a neutron star but a black hole. Particular attention is paid to the neutrino signals from these phenomena as a probe of hot dense matter.