Relevance theory is a cognitively-oriented pragmatic theory that aims at providing a psychologically realistic account of utterance interpretation. Originally developed by Dan Sperber and Deirdre Wilson (1995), it has in the last few decades been one of the leading frameworks for pragmatics research. In this chapter, I first present relevance theory's central claims and explain the motivations for them. I then review some of the main applications of relevance theory (linguistic underdetermination, the explicit-implicit distinction, lexical pragmatics and procedural meaning), and discuss some questions that are the focus of current research in these areas, both from within relevance theory and by advocates of alternative approaches such as semantic minimalism or indexicalism.