Several scholars have long suggested that human language and remarkable communicative abilities originate from the need and motivation to cooperate and coordinate actions with others. Yet, little work has focused on when and how great apes communicate during joint action tasks, partly because of the widely held assumption that animal communication is mostly manipulative, but also because non-human great apes' default motivation seems to be competitive rather than cooperative. Here, we review experimental cooperative tasks and show how situational challenges and the degree of asymmetry in terms of knowledge relevant for the joint action task affect the likelihood of communication. We highlight how physical proximity and strength of social bond between the participants affect the occurrence and type of communication. Lastly, we highlight how, from a production point of view, communicators appear capable of calibrating their signalling and controlling their delivery, showing clear evidence of first-order intentionality. On the other hand, recipients appear to struggle in terms of making use of referential information received. We discuss different hypotheses accounting for this asymmetry and provide suggestions concerning how future work could help us unveil to what degree the need for cooperation has shaped our closest living relatives' communicative behaviour. This article is part of the theme issue 'Revisiting the human 'interaction engine': comparative approaches to social action coordination'.