Punishment involves paying a cost to harm another individual and is thought to be a key mechanism that promotes cooperation. Nevertheless, it is not clear (1) whether punishment has the effect of converting cheats into cooperators or (2) how punishment can be favoured by selection, given that it involves costs to punishers. Here, I will use the cleaner fish-client mutualism as a model species to show that punishment does indeed promote cooperation in some contexts. However, I will go on to show that these results do not hold when we examine punishment in humans: instead, targets of punishment frequently respond with retaliation rather than with increased cooperation. I will also highlight an apparent paradox in the literature: the possibility of punishment promotes cooperation, despite the limited evidence to suggest that cheats become more cooperative in response to being punished. I will attempt to reconcile this apparent paradox by introducing a new hypothesis for punishment, based on viewing punishment as serving a competitive rather than a cooperation-enforcing function. This hypothesis also suggests an evolutionary route for 'punishment', that can account for antisocial punishment and punishment in one-shot settings, and doesn't require punishment to promote cooperation, nor the existence of group-level selection.