A key challenge in the field of human language evolution is the identification of the selective conditions that gave rise to language's generative nature. Comparative data on nonhuman animals provides a powerful tool to investigate similarities and differences among nonhuman and human communication systems and to reveal convergent evolutionary mechanisms. In this article, we provide an overview of the current evidence for combinatorial structures found in the vocal system of diverse species. We show that considerable structural diversity exits across and within species in the forms of combinatorial structures used. Based on this we suggest that a fine‐grained classification and differentiation of combinatoriality is a useful approach permitting systematic comparisons across animals. Specifically, this will help to identify factors that might promote the emergence of combinatoriality and, crucially, whether differences in combinatorial mechanisms might be driven by variations in social and ecological conditions or cognitive capacities.