There is and has been a fruitful flow of concepts and ideas between studies of learning in biological and artificial systems. Much early work that led to the development of reinforcement learning (RL) algorithms for artificial systems was inspired by learning rules first developed in biology by Bush and Mosteller, and Rescorla and Wagner. More recently, temporal-difference RL, developed for learning in artificial agents, has provided a foundational framework for interpreting the activity of dopamine neurons. In this Review, we describe state-of-the-art work on RL in biological and artificial agents. We focus on points of contact between these disciplines and identify areas where future research can benefit from information flow between these fields. Most work in biological systems has focused on simple learning problems, often embedded in dynamic environments where flexibility and ongoing learning are important, similar to real-world learning problems faced by biological systems. In contrast, most work in artificial agents has focused on learning a single complex problem in a static environment. Moving forward, work in each field will benefit from a flow of ideas that represent the strengths within each discipline.