Large-scale plasma instabilities with the potential of damaging wall structures or reducing their lifetime are a significant concern for magnetic confinement fusion. Among the most critical are disruptions and edge localized modes. Predicting the behavior of such instabilities and their control for ITER and beyond is a challenging task for which input from experiments, theory, and simulations is needed. This presentation describes non-linear MHD simulations of edge localized modes, disruptions and control strategies. The talk will explain why simulations or large-scale instabilities are needed and show that our simulations have already revealed a lot of aspects about the physics of large-scale instabilities. It will also give some insights into the actual work involved “behind the scenes” and challenges we are facing for the future.