Language is our legacy. It is the main evolutionary contribution of humans, and perhaps the most interesting trait that has emerged in the past 500 million years. Understanding how darwinian evolution gives rise to human language requires the integration of formal language theory, learning theory and evolutionary dynamics. Formal language theory provides a mathematical description of language and grammar. Learning theory formalizes the task of language acquisition—it can be shown that no procedure can learn an unrestricted set of languages. Universal grammar specifies the restricted set of languages learnable by the human brain. Evolutionary dynamics can be formulated to describe the cultural evolution of language and the biological evolution of universal grammar.