The assumption of self-interest has been quite central in classic theorizing of human cooperation. The present research focuses on two theoretical claims that challenge and complement this reasoning. The first claim is that people differ systematically in how they approach social dilemmas. Some people tend to cooperate, give others the benefit of doubt (prosocials), while other people primarily pursue their self-interest, either in absolute terms (individualists) or in relative terms (competitors). We discuss psychological and neuroscientific evidence showing that for prosocials, it is essential that they count on reciprocity. In contrast, for individualists, they may switch to cooperation if they come to be convinced that they can count on reciprocity. I also discuss recent field research showing a pronounced link with the choice to study psychology versus economics, political orientations, and "social mindfulness". The second claim is that social dilemma research often assumes that people always "see" the cooperative option, or that people are always "can" act in cooperative manner. This is not always true, and it are these circumstances that challenge cooperation in such a manner that we tend to overestimate self-interested motivation in others. I illustrate this claim with research on incompleteness of information in social dilemmas, and close by discussing a new program of research on cultural and genetic differences in trust.