In any given species, cooperation involves prosocial acts that usually return a fitness benefit to the actor. These acts are produced by a set of psychological rules, which will be similar in related species if they have a similar natural history of cooperation. Prosocial acts can be (i) reactive, i.e. in response to specific stimuli, or (ii) proactive, i.e. occur in the absence of such stimuli. We propose that reactive prosocial acts reflect sensitivity to (i) signals or signs of need and (ii) the presence and size of an audience, as modified by (iii) social distance to the partner or partners. We examine the evidence for these elements in humans and other animals, especially non-human primates, based on the natural history of cooperation, quantified in the context of food sharing, and various experimental paradigms. The comparison suggests that humans share with their closest living relatives reactive responses to signals of need, but differ in sensitivity to signs of need and cues of being watched, as well as in the presence of proactive prosociality. We discuss ultimate explanations for these derived features, in particular the adoption of cooperative breeding as well as concern for reputation and costly signalling during human evolution.