Humans have a sense of fairness, i.e. an interest in the ideal of equity. This sense allows them to compare their own efforts and subsequent outcomes with those of others, and thus to evaluate and react to inequity. The question is whether our closest living relatives, the non-human primates, show the behavioural characteristics that might qualify as necessary components to a sense of fairness, such as inequity aversion. In this article, we review the five different experimental approaches to studying behaviours related to fairness in non-human primates, including their underlying logic and main findings that represent the current state of research in this field. In the critical condition of all these studies, a subject and a conspecific partner have either to invest different efforts or receive different outcomes while observing each other. The main question is whether—and how—subjects react to unequal situations that humans would perceive as ‘unfair’. Taken together, the results from all five approaches provide only weak evidence for a sense of fairness in non-human primates. Although apes and monkeys are attentive to what the partner is getting, they do not seem to be able or motivated to compare their own efforts and outcomes with those of others at a human level. Even though the debate is still on-going, we believe that a full sense of fairness is not essential for cooperation. Obviously, apes and monkeys are capable of solving problems cooperatively, without a strong, humanlike sense of fairness. They are mainly interested in maximizing their own benefit, regardless of what others may receive. It is thus possible that a sense of fairness only exists rudimentarily in non-human primates.