Language is a uniquely human trait, and questions of how and why it evolved have been intriguing scientists for years. Nonhuman primates (primates) are our closest living relatives, and their behavior can be used to estimate the capacities of our extinct ancestors. As humans and many primate species rely on vocalizations as their primary mode of communication, the vocal behavior of primates has been an obvious target for studies investigating the evolutionary roots of human speech and language. By studying the similarities and differences between human and primate vocalizations, comparative research has the potential to clarify the evolutionary processes that shaped human speech and language. This review examines some of the seminal and recent studies that contribute to our knowledge regarding the link between primate calls and human language and speech. We focus on three main aspects of primate vocal behavior: functional reference, call combinations, and vocal learning. Studies in these areas indicate that despite important differences, primate vocal communication exhibits some key features characterizing human language. They also indicate, however, that some critical aspects of speech, such as vocal plasticity, are not shared with our primate cousins. We conclude that comparative research on primate vocal behavior is a very promising tool for deepening our understanding of the evolution of human speech and language, but much is still to be done as many aspects of monkey and ape vocalizations remain largely unexplored.