Vocalization is an ancient vertebrate trait essential to many forms of communication, ranging from courtship calls to free verse. Vocalizations may be entirely innate and evoked by sexual cues or emotional state, as with many types of calls made in primates, rodents and birds; volitional, as with innate calls that, following extensive training, can be evoked by arbitrary sensory cues in non-human primates and corvid songbirds; or learned, acoustically flexible and complex, as with human speech and the courtship songs of oscine songbirds. This review compares and contrasts the neural mechanisms underlying innate, volitional and learned vocalizations, with an emphasis on functional studies in primates, rodents and songbirds. This comparison reveals both highly conserved and convergent mechanisms of vocal production in these different groups, despite their often vast phylogenetic separation. This similarity of central mechanisms for different forms of vocal production presents experimentalists with useful avenues for gaining detailed mechanistic insight into how vocalizations are employed for social and sexual signalling, and how they can be modified through experience to yield new vocal repertoires customized to the individual's social group. This article is part of the theme issue 'What can animal communication teach us about human language?'