Human speech perception is a paradigm example of the complexity of human linguistic processing; however, it is also the dominant way of expressing vocal identity and is critically important for social interactions. Here, I review the ways that the speech, the talker, and the social nature of speech interact and how this may be computed in the human brain, using models and approaches from nonhuman primate studies. I explore the extent to which domain-general approaches may be able to account for some of these neural findings. Finally, I address the importance of extending these findings into a better understanding of the social use of speech in conversations.