Conversational implicatures (i) are implied by the speaker in making an utterance; (ii) are part of the content of the utterance, but (iii) do not contribute to direct (or explicit) utterance content; and (iv) are not encoded by the linguistic meaning of what has been uttered. In (1), Amelia asserts that she is on a diet, and implicates something different: that she is not having cake. (1)Benjamin:Are you having some of this chocolate cake?Amelia:I’m on a diet. Conversational implicatures are a subset of the implications of an utterance: namely those that are part of utterance content. Within the class of conversational implicatures, there are distinctions between particularized and generalized implicatures; implicated premises and implicated conclusions; and weak and strong implicatures. An obvious question is how implicatures are possible: how can a speaker intentionally imply something that is not part of the linguistic meaning of the phrase she utters, and how can her addressee recover that utterance content? Working out what has been implicated is not a matter of deduction, but of inference to the best explanation. What is to be explained is why the speaker has uttered the words that she did, in the way and in the circumstances that she did. Grice proposed that rational talk exchanges are cooperative and are therefore governed by a Cooperative Principle (CP) and conversational maxims: hearers can reasonably assume that rational speakers will attempt to cooperate and that rational cooperative speakers will try to make their contribution truthful, informative, relevant and clear, inter alia, and these expectations therefore guide the interpretation of utterances. On his view, since addressees can infer implicatures, speakers can take advantage of their ability, conveying implicatures by exploiting the maxims. Grice’s theory aimed to show how implicatures could in principle arise. In contrast, work in linguistic pragmatics has attempted to model their actual derivation. Given the need for a cognitively tractable decision procedure, both the neo-Gricean school and work on communication in relevance theory propose a system with fewer principles than Grice’s. Neo-Gricean work attempts to reduce Grice’s array of maxims to just two (Horn) or three (Levinson), while Sperber and Wilson’s relevance theory rejects maxims and the CP and proposes that pragmatic inference hinges on a single communicative principle of relevance. Conversational implicatures typically have a number of interesting properties, including calculability, cancelability, nondetachability, and indeterminacy. These properties can be used to investigate whether a putative implicature is correctly identified as such, although none of them provides a fail-safe test. A further test, embedding, has also been prominent in work on implicatures. A number of phenomena that Grice treated as implicatures would now be treated by many as pragmatic enrichment contributing to the proposition expressed. But Grice’s postulation of implicatures was a crucial advance, both for its theoretical unification of apparently diverse types of utterance content and for the attention it drew to pragmatic inference and the division of labor between linguistic semantics and pragmatics in theorizing about verbal communication.