Punishment and reputation-based mechanisms play a major role in supporting the evolution of human cooperation. Theoretical accounts and field observations suggest that humans use multiple tactics to intervene against offences-including confrontation, gossip and ostracism-which have unique benefits and costs. Here, we draw a distinction between direct punishment tactics (i.e. physical and verbal confrontation) and indirect reputation-based tactics (i.e. gossip and ostracism). Based on this distinction, we sketch the common and unique social functions that different tactics are tailored to serve and describe information-processing mechanisms that potentially underlie decisions concerning how to intervene against offences. We propose that decision rules guiding direct and indirect tactics should weigh information about the benefits of changing others' behaviour versus the costs of potential retaliation. Based on a synthesis of existing evidence, we highlight the role of situational, relational and emotional factors in motivating distinct punishment tactics. We suggest that delineating between direct and indirect tactics can inform debates about the prevalence and functions of punishment and the reputational consequences of third-party intervention against offences. We emphasize the need to study how people use reputation-based tactics for partner recalibration and partner choice, within interdependent relationships and social networks, and in daily life situations. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.