Humans care about having a positive reputation, which may prompt them to help in scenarios where the return benefits are not obvious. Various game-theoretical models support the hypothesis that concern for reputation may stabilize cooperation beyond kin, pairs or small groups. However, such models are not explicit about the underlying psychological mechanisms that support reputation-based cooperation. These models therefore cannot account for the apparent rarity of reputation-based cooperation in other species. Here, we identify the cognitive mechanisms that may support reputation-based cooperation in the absence of language. We argue that a large working memory enhances the ability to delay gratification, to understand others mental states (which allows for perspective-taking and attribution of intentions) and to create and follow norms, which are key building blocks for increasingly complex reputation-based cooperation. We review the existing evidence for the appearance of these processes during human ontogeny as well as their presence in non-human apes and other vertebrates. Based on this review, we predict that most non-human species are cognitively constrained to show only simple forms of reputation-based cooperation. This article is part of the theme issue The language of cooperation: reputation and honest signalling.