Neutrinos play a crucial role in determining fluid dynamics and nucleosynthesis in core-collapse supernovae and compact object mergers. Neutrino quantum kinetics, which governs their transport in phase space, interactions with matter, and flavor conversion (neutrino oscillations), is essential for developing realistic models of these phenomena. Accurately determining the neutrino radiation field, particularly in the presence of flavor conversion, requires solving the quantum kinetic equations, posing a formidable challenge in computational astrophysics. Nevertheless, remarkable progress has been achieved in recent years. In this seminar, I will provide an overview of these advances and discuss future prospects for incorporating flavor conversion effects into supernova and merger simulations.