Human language has long captured the imagination of biological researchers, but the gulf separating 'computation,' 'biology', and 'language' has been equally long-standing: the classical biological problem of how to bridge between a genotype and a phenotype, in this case, perhaps the most complex behavioral phenotype we know of. The aim of this talk is to show how recent developments in linguistic theory bridge this 'abstraction gap' by illuminating some of the modular design properties of human language, illustrating that despite its apparent surface complexity, human language's core seems to be far simpler than has been previously supposed, potentially reducible to a single, simple, basic operation that derives all the seemingly special properties of human language. Further, by positing this modular approach, we can shed light on the computational interfaces of human language to the systems of speech/motor production and parsing, as well as internal systems of inference; here there seems to be a natural, and expected kind of 'impedance matching,' with the design seemingly forced to follow constraints imposed by considerations of semantic interpretation, rather than considerations of computational complexity in parsing or production. Finally, this new modular view leads naturally to evolutionary considerations as to how these components arose in the course of evolution, in this case, a more 'saltational' view than is generally supposed.