To communicate, speakers need to make it clear what they are talking about. Referring expressions play a crucial part in achieving this, by anchoring utterances to things. Examples of referring expressions include noun phrases such as "this phenomenon", "it" and "the phenomenon to which this Topic is devoted". Reference is studied throughout the Cognitive Sciences (from philosophy and logic to neuro-psychology, computer science and linguistics), because it is thought to lie at the core of all of communication. Recent years have seen a new wave of work on models of referring, as witnessed by a number of recent research projects, books, and journal Special Issues. The Research Topic "Models of Reference" in Frontiers in Psychology is a new milestone, focusing on contributions from Psycholinguistics and Computational Linguistics. The articles in it are concerned with such issues as audience design, overspecification, visual perception, and variation between speakers.