Relevance Theory (RT) takes a cognitive-scientific approach to the study of human communication and utterance comprehension, but its roots lie in Grice’s philosophical analysis of speaker’s meaning and his account of “the logic of conversation.” The debt of RT (and of other current pragmatic theories) to Grice’s groundbreaking ideas cannot be overestimated. Work within RT pragmatics has also interacted with, influenced and been influenced by, much other work within the philosophy of language, in particular the multiple issues and concerns that have arisen in debates between advocates of minimalist and of contextualist accounts of truth-conditional semantics. Among the many issues that could be discussed here, I will focus on three in particular: (a) the proper domain of a pragmatic theory; (b) the role of pragmatics in grasping what a speaker explicitly communicates; (c) the priority of word sense conventions or of pragmatics in explaining linguistic communication.