Despite the significant attention that market manipulation has received in recent years many aspects of it are poorly understood. This article identifies from the theoretical and empirical literature what we do and do not know about market manipulation, and suggests directions for future research. We know that manipulation is possible and that it occurs in a wide variety of markets and circumstances. In contrast, we know little about how often manipulation occurs, its effects and how it responds to regulation. Suggested approaches for future research on these issues include: (1) collecting more comprehensive data sets of manipulation cases; (2) using detection controlled estimation methods to overcome sample selection and partial observability problems and (3) conducting controlled experiments. This article also constructs a novel and broad taxonomy of the different types of market manipulation and discusses approaches to defining manipulation.