This paper introduces a special issue of Language, Cognition and Neuroscience dedicated to Production of Referring Expressions: Models and Empirical Data, focusing on models of reference production that make empirically testable predictions, as well as on empirical work that can inform the design of such models. In addition to introducing the volume, this paper also gives an overview of recent experimental and modelling work, focusing on two principal aspects of reference production, namely, choice of anaphoric referential expression, and choice of semantic content for referential noun phrases. It also addresses the distinction between dialogue and non-dialogue settings, focussing especially on the impact of a dialogue setting on referential choice and the evidence for audience design in the choices speakers make.