Neural computational accounts of reward-learning have been dominated by the hypothesis that dopamine neurons behave like a reward-prediction error and thus facilitate reinforcement learning in striatal target neurons. While this framework is consistent with a lot of behavioral and neural evidence, this theory fails to account for a number of behavioral and neurobiological observations. In this special issue of EJN we feature a combination of theoretical and experimental papers highlighting some of the explanatory challenges faced by simple reinforcement-learning models and describing some of the ways in which the framework is being extended in order to address these challenges.