In the last twenty years a growing body of experimental evidence has posed a challenge to the standard Exponential Discounting Model of choice over time. Attention has focused on some specific 'anomalies', notably preference reversal and declining discount rates, leading to the formulation of the model of hyperbolic discounting which is finding increasing favour in the literature. In this paper we provide a survey of both the theoretical modelling and the experimental evidence relating to choice over time. As we will show, a careful analysis of the mapping between theoretical models and experimental investigations raises questions as to whether some of the most focused upon anomalies should be indeed classified as such, or whether they are really the most challenging ones for conventional theory. New developments are emerging both at the theoretical and empirical level, opening up new exciting avenues for investigation.