Human speech is marked by a signal–function decoupling, the capacity to produce sounds that can fulfil a variety of functions, in contrast to nonverbal vocalizations such as laughter, cries and screams, which are functionally more rigid. It has been argued that this decoupling provides an essential foundation for the emergence of language, in both ontogeny and phylogeny. Although language has a deep evolutionary history, whether this capacity for vocal functional flexibility also exists in the vocal systems of nonhuman animals has been much overlooked. Reasons are multiple. Here, we propose to diagnose the problems that have thus far hindered progress on understanding the evolutionary basis of functional flexibility, an issue which can shed broader light on the evolution of language. In particular, we aim to clarify what vocal functional flexibility is, why it matters, why we believe it should be investigated in nonhuman animals and how this could be best achieved.