Cartels remain widespread and constitute a major problem for society. Leniency policies reduce or cancel the sanctions for the first firm(s) that self-report being part of a cartel and have become the main enforcement instrument used by competition authorities around the world in their fight against cartels. Such policies have been shown to be a powerful tool in inducing firms to self-report or cooperate with a cartel investigation in exchange for a reduction in sanctions. Since they reduce sanctions for successful leniency applicants, these programs may also be abused to generate many successful convictions for the competition authority at the expense of reduced cartel deterrence and social welfare. Hence, it is vital for competition authorities and society to understand how leniency programs affect firms’ incentives, in order to optimize their design and administration. A rich theoretical, empirical and experimental economic literature has developed in the last two decades to meet the challenge. In this chapter, we review some of the key studies that have been undertaken to date, with emphasis on more recent contributions and without claiming to be exhaustive (we apologize in advance to the authors of papers we could not discuss), highlighting and comparing the main results, and setting out their limitations. We conclude with a general assessment and an agenda for future research on this topic at the core of competition policy.