How should we best analyse the meaning of proper names, indexicals, demonstratives, both simple and complex, and definite descriptions? In what relation do such expressions stand to the objects they designate? In what relation do they stand to mental representations of those objects? Do these expressions form a semantic class, or must we distinguish between those that arc referential and those that are quantificational? Such questions have constituted one of the core research areas in the philosophy of language for much of the last century, yet consensus remains elusive: the field is still divided, for instance, between those who hold that all such expressions are semantically descriptive and those who would analyse most as the natural language counterparts of logical individual constants. The aim of this thesis is to cast new light on such questions by approaching them from within the cognitive framework of Sperber and Wilson's Relevance Theory. Relevance Theory offers not just an articulated pragmatics but also a broad conception of the functioning of natural language which differs radically from that presupposed within (most of) the philosophy of language. The function of linguistic expressions, on this conception, is not to determine propositional content, but rather to provide inferential premises which, in parallel with context and general pragmatic principles, will enable a bearer to reach the speaker's intended interpretation. Working within this framework, I shall argue that the semantics of the expressions discussed should best be analysed not in terms of their relation to those objects which, on occasions of use, they may designate, but rather in terms of the indications they offer a hearer concerning the mental representation which constitutes the content of a speaker's informative intention. Such an analysis can, I shall claim, capture certain key data on reference which have proved notoriously problematic, while respecting a broad range of apparently conflicting intuitions.