Following the observation that vervet monkeys are capable of labelling different predator types with their vocalizations, comparative research in language evolution gained increasing interest. Over the last four decades, an impressive body of data has since accumulated demonstrating that many features of language can be found in the communication systems of nonhuman primates. One stumbling block to the phylogenetic reconstruction of language, however, has been language’s syntactic layer. We specifically highlight that, whilst current studies provide promising evidence for syntactic-like structures in the communication systems of monkeys, reconstructing the evolutionary origins of syntax hinges on comparable data from our closest-living relatives, the great apes. We critically assess existing data on potential candidates for combinatorial structures in the great ape clade and conclude that further experimental investigation is crucial to validating preliminary observational findings.