We study two types of supernovae -Type IA (SNIa) and Core-collapse supernovae (CCSNe), particularly how they may help to probe new physics. First, using a two-dimensional hydrodynamics code with a fifth-order shock capturing scheme, we simulate the explosions of dark matter admixed SNIa and find that the explosion energy and abundance of 56 Ni produced are sensitive to the mass of admixed dark matter. A small admixture of dark matter may account for some sub-luminous SNIa observed. Second, by incorporating a hybrid equation of state (EOS) that includes a hadron-to-quark phase transition, we study possible formation of quark stars in CCSNe. We calculate the gravitational-wave and neutrino emissions from such a system, and we study the effects of the parameters in the EOS on such signals.