 Montague semantics is a theory of natural language semantics and of its relation with syntax. It was originally developed by the logician Richard Montague (1930–1971) and subsequently modified and extended by linguists, philosophers, and logicians. The most important features of the theory are its use of model theoretic semantics which is nowadays commonly used for the semantics of logical languages and its adherence to the principle of compositionality—that is, the meaning of the whole is a function of the meanings of its parts and their mode of syntactic combination. This entry presents the origins of Montague Semantics, summarizes important aspects of the classical theory, and sketches more recent developments. We conclude with a small example, which illustrates some modern features.