Responding to wrongdoing is a core feature of our social lives. Indeed, a central assumption of modern institutional justice systems is that transgressors should be punished. In this Review, we synthesize the developmental literature on third-party intervention to provide insight into the types of responses to transgressions that are privileged early in ontogeny. In particular, we focus on young children as both assessors and agents of third-party punishment. With respect to assessment, children have rich expectations about the pursuit of punishment and evaluate those who punish transgressors positively. With respect to agency, children punish wrongdoing even when doing so is costly, and their motives to do so are tethered to a variety of concerns (such as retribution and restoration). Our Review suggests that key concepts in modern institutional justice systems are apparent in early child development, and that third-party punishment is a signature of children’s sophisticated toolkit for regulating social relationships and behaviour.