The comparative approach can provide insight into the evolution of human speech, language and social communication by studying relevant traits in animal systems. Bats are emerging as a model system with great potential to shed light on these processes given their learned vocalizations, close social interactions, and mammalian brains and physiology. A recent framework outlined the multiple levels of investigation needed to understand vocal learning across a broad range of non-human species, including cetaceans, pinnipeds, elephants, birds and bats. Here, we apply this framework to the current state-of-the-art in bat research. This encompasses our understanding of the abilities bats have displayed for vocal learning, what is known about the timing and social structure needed for such learning, and current knowledge about the prevalence of the trait across the order. It also addresses the biology (vocal tract morphology, neurobiology and genetics) and evolution of this trait. We conclude by highlighting some key questions that should be answered to advance our understanding of the biological encoding and evolution of speech and spoken communication. This article is part of the theme issue 'What can animal communication teach us about human language?'