According to a number of researchers in linguistics and artificial intelligence, the key to the meanings of expressions such as in other words, that is, and for example/for instance lies in the particular coherence relations they express in discourse. It is argued that these relations are sub-types of the relation of Elaboration and hence are ideational or semantic relations which express some experience of the world about us and within our imagination. In this paper I argue that the notion of Elaboration does not provide an adequate theoretical basis for the analysis of these expressions. I show, first, that their analysis in terms of ideational relations cannot capture the way in which utterances that contain them are understood, and, second, that the phenomena which are said to fall under the relation of Elaboration do not in fact constitute a single class. I show that Sperber and Wilson’s (1986) relevance theoretic pragmatics provides a better explanatory framework for the analysis of these expressions, arguing that while their notion of interpretive resemblance plays a central role in the analysis of some utterances, there are other cases which must be analysed in terms of inferential relations between propositions. In all cases, the question of how the utterance is to be understood does not depend on the classification of the coherence relation it exhibits but on how it achieves relevance.