Both in linguistics and in psycholinguistics there is some debate about how rich or thin lexico-semantic representations are. Traditionally, in formal semantics but also in philosophy of language as well as in cognitive pragmatics, lexical meanings have been thought to be simple stable denotations or functions. In this paper, we present and discuss a number of interpretational phenomena of which the analysis proposed in the literature makes crucial use of rich meanings. The phenomena in question are cases where the assignment of truth-conditional contents to utterances seems to follow rules that do not operate on simple stable denotations or any other kind of ‘thin’ meanings but where composition takes rich structured representations as input. We also discuss problems for such accounts, which are mostly based on the inability of extant rich meanings accounts to explain many other interpretational phenomena, and we discuss the solutions that have been proposed to solve them. Furthermore, we address the discussion whether the informationally rich meanings are part of semantics, and more specifically part of the lexicon, or whether this information should be ascribed to more general world knowledge.