Reciprocity is probably one of the most debated theories in evolutionary research. After more than 40 years of research, some scientists conclude that reciprocity is an almost uniquely human trait mainly because it is cognitively demanding. Others, however, conclude that reciprocity is widespread and of great importance to many species. Yet, it is unclear how these species reciprocate, given its apparent cognitive complexity. Therefore, our aim was to unravel the psychological processes underlying reciprocity. By bringing together findings from studies investigating different aspects of reciprocity, we show that reciprocity is a rich concept with different behavioural strategies and cognitive mechanisms that require very different psychological processes. We reviewed evidence from three textbook examples, i.e. the Norway rat, common vampire bat and brown capuchin monkey, and show that the species use different strategies and mechanisms to reciprocate. We continue by examining the psychological processes of reciprocity. We show that the cognitive load varies between different forms of reciprocity. Several factors can lower the memory demands of reciprocity such as distinctiveness of encounters, memory of details and network size. Furthermore, there are different information operation systems in place, which also vary in their cognitive load due to assessing the number of encounters and the quality and quantity of help. We conclude that many species possess the psychological processes to show some form of reciprocity. Hence, reciprocity might be a widespread phenomenon that varies in terms of strategies and mechanisms.