Reinforcement learning (RL) refers to the scientific study of how animals and machines adapt their behavior in order to maximize reward. The history of RL research can be traced to early work in psychology on instrumental learning behavior. However, the modern field of RL is a highly interdisciplinary area that lies that the intersection of ideas in computer science, machine learning, psychology, and neuroscience. This chapter summarizes the key mathematical ideas underlying this field including the exploration/exploitation dilemma, temporal-difference (TD) learning, Q-learning, and model-based versus model-free learning. In addition, a broad survey of open questions in psychology and neuroscience are reviewed.