This chapter argues that an evolutionary cultural approach to language not only has already proven fruitful, but it probably holds the key to understand many puzzling aspects of language, its change and origins. The chapter begins by highlighting several still common misconceptions about language that might seem to call into question a cultural evolutionary approach. It explores the antiquity of language and sketches a general evolutionary approach discussing the aspects of function, fi tness, replication, and selection, as well the relevant units of linguistic evolution. In this context, the chapter looks at some fundamental aspects of linguistic diversity such as the nature of the design space, the mechanisms generating it, and the shape and fabric of language. Given that biology is another evolutionary system, its complex coevolution with language needs to be understood in order to have a proper theory of language. Throughout the chapter, various challenges are identifi ed and discussed, sketching promising directions for future research. The chapter ends by listing the necessary data, methods, and theoretical developments required for a grounded evolutionary approach to language.