Recent theoretical development of collapse-driven supernova explosion is reviewed. In particular, we discuss in detail i) convection in the hot bubble region above the proto-neutron star as the source of the large amplitude velocity fluctuations which is necessary to explain large scale mixing in SN1987A, and ii) jet-like explosion induced by axisymmetric neutrino emission from a rotating oblate proto-neutron star, which might account for asymmetry of expanding envelope of SN1987A.