Language as a computational cognitive mechanism appears to be unique to the human species. However, there are remarkable behavioral similarities between song learning in songbirds and speech acquisition in human infants that are absent in non-human primates. Here we review important neural parallels between birdsong and speech. In both cases there are separate but continually interacting neural networks that underlie vocal production, sensorimotor learning, and auditory perception and memory. As in the case of human speech, neural activity related to birdsong learning is lateralized, and mirror neurons linking perception and performance may contribute to sensorimotor learning. In songbirds that are learning their songs, there is continual interaction between secondary auditory regions and sensorimotor regions, similar to the interaction between Wernicke’s and Broca’s areas in human infants acquiring speech and language. Taken together, song learning in birds and speech acquisition in humans may provide useful insights into the evolution and mechanisms of auditory-vocal learning.