We report a recent status of multi-dimensional neutrino-radiation hydrodynamics simulations for clarifying the explosion mechanism of core-collapse supernovae (CCSNe). In this contribution, we present two results, one from two-dimensional (2D) simulations using multiple progenitor models and another from three-dimensional (3D) rotational core-collapse simulation using a single progenitor. From the first ever systematic 2D simulations, it is shown that the compactness parameter ξ that characterizes the structure of the progenitors is a key to diagnose the explodability of neutrino-driven explosions. In the 3D rotating model, we find a new type of rotation-assisted explosion, which makes the explosion energy bigger than that in the non-rotating model. The unique feature has not been captured in previous 2D self-consistent rotational models because the growth of non-axisymmetric instabilities is the key to foster the explosion by enhancing the energy transport from the proto-neutron star to the gain region.
