Rewards are fundamental to everyday life. They confer pleasure, support learning, and mediate decisions. Dopamine-releasing neurons in the midbrain are critical for reward processing. These neurons receive input from more than 30 brain areas and send widespread projections to the basal ganglia and frontal cortex. Their phasic responses are tuned to rewards. Specifically, dopamine signals code reward prediction error, the difference between received and predicted rewards. Decades of research in awake, behaving non-human primates (NHP), have shown the importance of these neural signals for learning and decision making. In this review, we will provide an overview of the bedrock findings that support the reward prediction error hypothesis and examine evidence that this signal plays a role in learning and decision making. In addition, we will highlight some of the conceptual challenges in dopamine neurophysiology and identify future areas of research to address these challenges. Keeping with the theme of this special issue, we will focus on the role of NHP studies in understanding dopamine neurophysiology and make the argument that primate models are essential to this line of research.