The goal of this paper is to analyze the notion of “compositionality” and its use in contemporary cognitive science. We argue that the concept has undergone a series of apparently minor definitional shifts since its initial inception within the field of philosophy of language (as indicated by Janssen, 2012). These changes result in a divergent meaning of the term as it is used in the emergent communication and language evolution communities. Hitherto, this fact has been underappreciated, whereas we believe that it has significant implications for understanding the nature of syntax and the sources of linguistic and conceptual structure. We argue that originally, “compositionality” was understood as pertaining primarily to the process of understanding a compound utterance by a hearer. Other scholars, however, take it to be a prerequisite of the structure of languages. In all contexts, investigating compositionality of natural languages requires making a host of idealizing assumptions. For this reason, we propose to understand compositionality as just one idealized principle influencing the construction of compound expressions in language, necessarily complemented by other principles. This allows for appreciating the structural entanglements permeating natural language and opens new avenues for accounting for them.