An increasingly popular animal model for studying the neural basis of social behavior, cognition, and communication is the common marmoset (Callithrix jacchus). Interest in this New World primate across neuroscience is now being driven by their proclivity for prosociality across their repertoire, high volubility, and rapid development, as well as their amenability to naturalistic testing paradigms and freely moving neural recording and imaging technologies. The complement of these characteristics set marmosets up to be a powerful model of the primate social brain in the years to come. Here, we focus on vocal communication because it is the area that has both made the most progress and illustrates the prodigious potential of this species. We review the current state of the field with a focus on the various brain areas and networks involved in vocal perception and production, comparing the findings from marmosets to other animals, including humans.