Group-living primates are likely to spend a substantial amount of time grooming and resting with a small number of other group members. Such close and enduring relationships are regarded as affiliative. The properties of affiliative relationships are not fully understood and no consensus exists on how to quantitatively describe them. In this review, I explain the primate behaviors that are related to affiliative relationships and examine the means for using these behaviors to measure the relationship. Traditionally, affiliative relationships are defined by the frequency of proximity and grooming. Individuals with frequent proximity and grooming tend to perform altruistic behaviors for their partners without immediate return from them, groom each other in a reciprocal manner in the long-term, show distress and reconcile after agonistic interactions, and synchronize their behaviors with those of their partners. Thus, in addition to measuring the frequencies of proximity and grooming, these behavioral tendencies might be used as indices of affiliative relationships. Similarly, other questions concerning affiliative relationships remain unexplained. Some studies show that affiliative relationships increase reproductive success, but the mechanisms leading to fitness outcomes remain unclear. Although typically in primates, related individuals tend to form affiliative relationships, such relationships are also formed with unrelated individuals. Affiliative relationships could mitigate the negative effects of competition among individuals in large social groups and ensure that the individuals that form the relationship receive benefits from each other (e.g., agonistic support and collective mobbing). It is also unclear whether the affiliated relationships of nonhuman primates are equivalent to those of humans. Further research is necessary to elucidate similarities or differences in affiliative relationships between human and nonhuman primates.