Language, humans’ most distinctive trait, still remains a ‘mystery’ for evolutionary theory. It is underpinned by a universal infrastructure—cooperative turn-taking—which has been suggested as an ancient mechanism bridging the existing gap between the articulate human species and their inarticulate primate cousins. However, we know remarkably little about turn-taking systems of non-human animals, and methodological confounds have often prevented meaningful cross-species comparisons. Thus, the extent to which cooperative turn-taking is uniquely human or represents a homologous and/or analogous trait is currently unknown. The present paper draws attention to this promising research avenue by providing an overview of the state of the art of turn-taking in four animal taxa—birds, mammals, insects and anurans. It concludes with a new comparative framework to spur more research into this research domain and to test which elements of the human turn-taking system are shared across species and taxa.