I argue that many of the pragmatic notions that are commonly attributed to H. P. Grice, or are reported to be inspired by his work on pragmatics, such as assertion, conventional implicature, cooperation, common ground, common knowledge, presuppositions and conversational strategies, have their origins in C. S. Peirce’s theory of signs and his pragmatic logic and philosophy. Both Grice and Peirce rooted their theories in normative rationality, anti-psychologism and the relevance of assertions. With respect to the post-Gricean era of pragmatics, theories of relevance may be seen to have been geared, albeit unconsciously, upon Peirce’s pragmatic agenda.