Affinitive contact between former opponents soon after a conflict has been demonstrated in a growing number of primate species. Several recent studies show that such contact reduces the probability of future conflicts, allows the recipient of aggression to reduce its anxiety, and restores tolerance between former opponents. Hence, these contacts can be termed reconciliation. In this paper, we critically discuss common methodological problems of studying reconciliation, examine functional aspects, and evaluate the existing variation in primate reconciliation in light of predictions derived from four untested hypotheses about its evolutionary origins. We find that the occurrence of reconciliation in primates is not limited to anthropoids. Neither is it limited to species with formalized dominance relations. Reconciliation is also not a prerequisite for life in permanent social groups. Instead, several lines of evidence support the hypothesis that reconciliation serves to maintain valuable social relationships between individuals. We suggest several more specific versions of this hypothesis and discuss reconciliation between kin, mates, and alliance partners, as well as a number of open questions pertaining to the mechanisms, functions and origins of reconciliation among primates.