The collapse of dense cores in massive stars proceeds as follows. Initially, leptons dominate the pressure because neutrinos become trapped at high densities. This results in the formation of a cool inner core that collapses homologously. At around nuclear densities the pressure from nucleons increases rapidly and halts the collapse, giving a core bounce. A shock forms at the surface of the inner core and propagates into the infalling envelope. These basic features have emerged in the hydrodynamic studies of collapse by various researchers. However, the question of final outcome of collapse is unresolved at present. The evolution of the core after the shock has propagated through the envelope has not been addressed in detail. This communication summarizes some current results of the author's ongoing study of stellar collapse.