In recent years a large number of experimental studies have documented the existence of strong reciprocity among humans. Strong reciprocity means that people willingly repay gifts and punish the violation of cooperation and fairness norms even in anonymous one-shot encounters with genetically unrelated strangers. We provide ethnographic and experimental evidence suggesting that ultimate theories of kin selection, reciprocal altruism, costly signalling and indirect reciprocity do not provide satisfactory evolutionary explanations of strong reciprocity. The problem of these theories is that they can rationalize strong reciprocity only if it is viewed as maladaptive behavior whereas the evidence suggests that it is an adaptive trait. Thus, we conclude that alternative evolutionary approaches are needed to provide ultimate accounts of strong reciprocity.