Studying corruption presents unique challenges. Recent work in the spirit of computational social science exploits newly available data and methods to give a fresh perspective on this important topic. In this chapter we highlight some of these works, describing how they provide insights into classic social scientific questions about the structure and dynamics of corruption in society from micro to macro scales. We argue that corruption is fruitfully understood as a collective action problem that happens between embedded people and organizations. Computational methods like network science and agent-based modeling can give insights into such situations. We also present various (big) data sources that have been exploited to study corruption. We conclude by highlighting work in adjacent fields, for instance on the problems of collusion, tax evasion, organized crime, and the darkweb, and promising avenues for future work.