The traditional definition of anaphora in purely co-textual terms as a relation between two co-occurring expressions is in wide currency in theoretical and descriptive studies of the phenomenon. Indeed, it is currently adopted in on-line psycholinguistic experiments on the interpretation of anaphors, and is the basis for all computational approaches to automatic anaphor resolution (see Mitkov 2002). Under this conception, the anaphor, a referentially-dependent expression type, requires "saturation" by an appropriate referentially-autonomous, lexically-based expression — the antecedent — in order to achieve full sense and reference. However, this definition needs to be re-examined in the light of the ways in which real texts operate and are understood, where the resulting picture is rather different. The article aims to show that the co-textual conception is misconceived, and that anaphora is essentially an integrative, discourse-creating procedure involving a three-way relationship between an "antecedent trigger", an anaphoric predication, and a salient discourse representation. It is shown that it is only in terms of a dynamic interaction amongst the interdependent dimensions of text and discourse, as well as context, that the true complexity of anaphoric reference may be satisfactorily described. The article is intended as a contribution to the broader debate between the formalist and the functionalist accounts of language structure and use.