Section 1 is a general introduction to the theories discussed in the paper, primarily Sperber and Wilson's relevance theory, with its distinction between “implicature” and “explicature”, and Grice's theory of conversational principles and implicature. Section 2 discusses specific types of implicatures that must be approached in a different manner that the implicatures most commonly discussed in the literature. It is argued that some of these implicatures are hard to explain in the context of relevance theory. To this group of implicatures belong those arising from communicating information by repeating information already known to the listener, and from communicating information and humor by ironic understatement. Section 3 examines the division between explicatures and implicatures. Specifically, the definition of this division is dependent on Sperber and Wilson's assumptions about the division between a person's mental lexicon and his encyclopedic knowledge of the world. However, it is shown that the latter division is both philosophically and practically troublesome. Section 4 asks whether it is even possible to define the division between lexical and general knowledge. The conclusion of the present paper is that it is not.