The Kurdish language is an integral component of any conceptualisation of “Kurdishness”, but just what constitutes Kurdish remains highly disputed. In this introduction, we take up a number of key questions relating to Kurdish (e.g. whether it is one or more than one language, which varieties should be considered under Kurdish, what are its origins, etc.), discussing them in the light of contemporary linguistics. A critical assessment of the notions of “language” and “dialect” is followed by a review of different approaches to classifying Kurdish, and exemplified through the case-study of Zazaki. We suggest that a good deal of the confusion arises through a failure to distinguish different kinds of linguistic evidence (in a narrow sense), from the results of socially contracted and negotiated perceptions of identity, rooted in shared belief systems and perceptions of a common history. We then present an overview of recent trends in Kurdish linguistics and attempt to identify some of the most pressing research desiderata.