The language sciences are about to undergo dramatic changes. The cognitive sciences have taken their object of enquiry to be the characterization of The Human Mind, and the language sciences have focused on the characterization of The Language Instinct, or Universal Grammar. This abstraction away from variation and diversity is now significantly inhibiting research – after all, diversity at all levels is a unique feature of our communication system compared to all other species. Further, the universals which have been the goal of linguistic research have evaporated in the face of increasing information about linguistic diversity and language change. The alternative Darwinian paradigm embraces the new facts about cognitive and linguistic diversity, viewing variation as the fuel for evolution, and adopts a diachronic perspective in which we can ask about the relative roles of biological and cultural evolution and their interaction. New findings suggest that language diversity is largely a product of cultural evolution under the constraints of general cognitive capacities rather than being tightly constrained by either Universal Grammar or Greenbergian universals.