Animals often aid others without gaining any immediate benefits. Although these acts seem to reduce the donor's fitness, they are only apparently altruistic. Donors typically help because they or their kin receive future benefits or avoid costly punishment. Reciprocal altruism--alternating the roles of donor and recipient--has been a well-studied form of cooperation among non-kin because of its intuitive appeal in explaining human cooperation. Despite immense theoretical interest, little empirical evidence substantiates the biological importance of reciprocal altruism in non-human animals. We propose that this is because psychological mechanisms constrain its application in cooperative contexts. In particular, we contend that cognitive limitations such as temporal discounting, numerical discrimination and memory make reciprocity difficult for animals.