This article focuses on claims about the origin and evolution of language from the point of view of the formalist–functionalist debate in linguistics. In linguistics, an account of a grammatical phenomenon is considered “formal” if it accords center stage to the structural properties of that phenomenon, and “functional” if it appeals to the language user's communicative needs or to domain‐general human capacities. The gulf between formalism and functionalism has been bridged in language evolution research, in that some leading formalists, Ray Jackendoff for one, appeal to functional mechanisms such as natural selection. In Jackendoff's view, the biological evolution of language has proceeded in stages, each stage improving communicative efficiency. This article calls into question that idea, pointing to the fact that well‐understood purely historical processes suffice to explain the emergence of many grammatical properties. However, one central aspect of formalist linguistic theorizing—the idea of the autonomy of syntax—poses a challenge to the idea, central to most functionalist approaches, that the nature of grammar is a product of purely historical (as opposed to biological) evolution. The article concludes with a discussion of the origins of the autonomy of syntax, speculating that it may well have arisen over evolutionary (as opposed to historical) time.