“Semantics” can mean quite different things in different contexts. There are many reasons to be interested in meaning, and it can be studied from many perspectives. The history of formal semantics over the last 50 years is a story of collaboration among linguists, logicians, and philosophers. One central figure was the logician and philosopher Richard Montague, a student of Tarski’s, whose seminal works on the formal semantics of natural language date from the late 1960’s and early 1970’s. Starting in the 1970s, philosophers and especially linguists worked to integrate Montague’s semantics with Chomskyan syntax. Substantive progress was rapid and has been successful, but there were foundational questions that have remained unresolved. While Chomsky and most linguists view linguistics as a cognitive science, the Fregean tradition in which Montague worked is strongly anti-psychologistic. Linguists who do formal semantics have generally also seen themselves as contributing to cognitive science, but this seems to require, at least implicitly, some rethinking of the traditional Chomskyan notion of “the competence of the native speaker”. The history of these foundational issues in formal semantics, including the question of whether meanings are “in the head” suggests that we are moving toward a less “narrowly psychological” view of what it is to know a language.