This chapter discusses a major contribution that Noam Chomsky made to the study of human language, which was to consider human languages in terms of generative, formalized rule systems, i.e., a formal grammar. Chomsky established a hierarchy of grammar types that differ in their so-called generative capacity, which allowed him and others to locate what kind of formal grammar within this hierarchy is needed for human languages. This hierarchy also proved useful in defining the grammars that are needed for computer languages or “languages” of nonhuman species (or even imaginable artificial or mathematical “languages”), and thus found applications in many other areas. We will ask what kinds of formal grammars can be taken as models of the mental grammars that language learners construct, considering recent developments in both formal language theory and the theory of natural language syntax. We will see that the field of formal language theory is a vibrant area of linguistics that continues to develop new methods and applications not only to syntax, but also to phonology. We will also ask whether formal language theory sheds light on the hypothesized innate language capacity.