This proposal brings together scientific teams working from a variety of perspectives on one of the defining features of human cognition - referential communication. This ability was once thought to be uniquely human. But recent research suggests that other species, including not only primates but also more distant evolutionary relations, have evolved referential signals. Our starting point is that human referential communication should be conceived of not as one ability supported by a single mechanism, but as a complex function that results from the integration of diverse mechanisms that may have different evolutionary origins. Understanding referentiality requires an analysis of its component skills and how they can be articulated into systems of varying complexity. This can be best achieved through a crossdisciplinary comparative evolutionary approach. Our aim is to implement such an approach tracking the evolutionary origins of some of the key components of referentiality and the diverse ways in which they are realised and combined by evolution. We propose a set of empirical projects aimed at gathering innovative evidence on referential signals in various species of primates (including humans) and non-primates. These combine observational and experimental studies in the wild and in captivity exploring the semantic flexibility of referential calls in monkeys, dolphins, and parrots, the use of referential calls and referential gestures in great apes and canids, and their combination with skills such as Theory of mind to govern their strategic use. Our proposal unifies concepts and methods, and applies similar tests across species to guarantee the comparability of data. The empirical studies are integrated with two overarching theoretical projects aimed at reassessing the notion of referential communication and proposing a model of how and why the unique ways of human referential communication evolved.