The Bullet Cluster, Pandora's Cluster, the Trainwreck Cluster - merging galaxy clusters are some of the most spectacular events in the Universe, the most energetic things to occur since the Big Bang. Because these systems are very far from equilibrium, interpreting their observations is much more challenging than in their relaxed counterparts. Powered by idealised and numerical simulations, however, they are uniquely powerful in constraining such properties as the self-interaction cross-section of dark matter, the viscosity of the intracluster medium and the strength of cosmic magnetic fields. Due to their enhanced triaxiality, they are also the most potent gravitational lenses in the Universe, revealing the galaxy and quasar populations otherwise too faint to observe, including now several candidates just half a billion years after the Big Bang. In this talk, I show examples of each of these use cases, and show how the path forward is being accelerated with machine learning and simulation-based inference.