The large neutrino flux emitted during core-collapse supernovae leads to non-negligible neutrino self-interactions. The presence of neutrino self-interaction is the cause of interesting non-linear evolution of neutrino flavor. This offers a unique probe for neutrino properties. Collective neutrino oscillations are also essential for understanding some aspects of the physics of supernovae. Due to the non-linear nature of the equations of motion, there are challenges involved in the computation of flavor evolution even in the simplest case. I will discuss the physics impact of supernova neutrinos, the challenges involved, and what the future holds for the study of supernova neutrinos.