Research is reviewed that addresses itself to human language learning by developing precise, mechanistic models that are capable in principle of acquiring languages on the basis of exposure to linguistic data. Such research includes theorems on language learnability from mathematical linguistics, computer models of language acquisition from cognitive simulation and artificial intelligence, and models of transformational grammar acquisition from theoretical linguistics. It is argued that such research bears strongly on major issues in developmental psycholinguistics, in particular, nativism and empiricism, the role of semantics and pragmatics in language learning, cognitive development, and the importance of the simplified speech addressed to children.