Neutrinos are known to play important roles in many astrophysical scenarios from the early period of the big bang to current stellar evolution being a unique messenger of the fusion reactions occurring in the center of our sun. In particular, neutrinos are crucial in determining the dynamics and the composition evolution in explosive events such as core-collapse supernovae and the merger of two neutron stars. In this paper, we review the current understanding of supernovae and binary neutron star mergers by focusing on the role of neutrinos therein. Several recent improvements on the theoretical modeling of neutrino interaction rates in nuclear matter as well as their impact on the heavy element nucleosynthesis in the supernova neutrino-driven wind are discussed, including the neutrino-nucleon opacity at the mean field level taking into account the relativistic kinematics of nucleons, the effect due to the nucleon-nucleon correlation, and the nucleon-nucleon bremsstrahlung. We also review the framework used to compute the neutrino-nucleus interactions and the up-to-date yield prediction for isotopes from neutrino nucleosynthesis occurring in the outer envelope of the supernova progenitor star during the explosion. Here improved predictions of energy spectra of supernova neutrinos of all flavors have had significant impact on the nucleosynthesis yields. Rapid progresses in modeling the flavor oscillations of neutrinos in these environments, including several novel mechanisms for collective neutrino oscillations and their potential impacts on various nucleosynthesis processes are summarized.