Empathy, the capacity to share and understand others’ states, is crucial for facilitating enduring social relationships and managing ingroup and outgroup dynamics. Despite being at the center of much scrutiny and debate in human research, the evolutionary foundations of empathy remain relatively opaque. Moreover, inconsistencies remain regarding definitions and theoretical models, leading to discrepancies in how to systematically represent and address empathy and understand its evolutionary basis. As a complex, multi-dimensional phenomenon, certain components of empathy are likely to be evolutionarily ancient whereas others may be more derived. As our closest living relatives, nonhuman primates provide an opportunity to explore the evolutionary origins of empathy and its subcomponents. Due to the rich diversity of primate societies, we can comparatively study evidence of affective responding and empathic behaviour within the context of different social dynamics and organisation. Although studies have been conducted on individual primate species, especially the great apes, direct species comparisons are rare. Here we examine the literature investigating evidence for empathy among primates focussing on its underlying affective and cognitive components. In reviewing the literature, we also highlight species that need more coverage to enhance our overall understanding of how empathy has evolved within the primate order.