This article offers a survey of computational research on referring expressions generation (REG). It introduces the REG problem and describes early work in this area, discussing what basic assumptions lie behind it, and showing how its remit has widened in recent years. We discuss computational frameworks underlying REG, and demonstrate a recent trend that seeks to link up REG algorithms with well-established Knowledge Representation traditions. Considerable attention is given to recent efforts at evaluating REG algorithms and the lessons that they allow us to learn. The article concludes with a discussion of the way forward in REG, focussing on references in larger and more realistic settings.