Neutron-star mergers and core-collapse supernovae are promising events to herald a new era of multi-messenger astronomy, as they release substantial amounts of energy in gravitational waves, neutrinos, and electromagnetic emission. Moreover, these events are connected to long-standing physics questions related to, e.g., heavy-element nucleosynthesis, gamma-ray bursts, and the nuclear equation of state. However, while offering a unique laboratory to investigate matter and spacetime under extreme conditions, these events are particularly difficult to model theoretically, one of the most challenging, but equally important ingredients being the neutrino transport. The latter is not only responsible for cooling the compact remnant and heating its surroundings, but it may also have a major leverage on the nucleosynthesis conditions in the ejecta and the eventual launch of a polar jet. In this talk I will review the current state-of-the-art in modeling mergers and core-collapse supernovae and present some recent results that we obtained from numerical simulations.