J. J. Gibson's concept of affordance, one of the central pillars of ecological psychology, is a truly remarkable idea that provides a concise theory of animal perception predicated on environmental interaction. It is thus not surprising that this idea has also found its way into robotics research as one of the underlying theories for action perception. The success of the theory in this regard has meant that existing research is both abundant and diffuse by virtue of the pursuit of multiple different paths and techniques with the common goal of enabling robots to learn, perceive and act upon affordances. Up until now there has existed no systematic investigation of existing work in this field. Motivated by this circumstance, in this article we begin by defining a taxonomy for computational models of affordances rooted in a comprehensive analysis of the most prominent theoretical ideas of import in the field. Subsequently, after performing a systematic literature review, we provide a classification of existing research within our proposed taxonomy. Finally, by both quantitatively and qualitatively assessing the data resulting from the classification process, we highlight gaps in the research terrain and outline open questions for the investigation of affordances in robotics that we believe will help inform future work, prioritize research goals, and potentially advance the field towards greater robot autonomy.Prepared using sagej.cls [Version: 2015/06/09 v1.01]