Reward prediction errors consist of the differences between received and predicted rewards. They are crucial for basic forms of learning about rewards and make us strive for more rewards—an evolutionary beneficial trait. Most dopamine neurons in the midbrain of humans, monkeys, and rodents signal a reward prediction error; they are activated by more reward than predicted (positive prediction error), remain at baseline activity for fully predicted rewards, and show depressed activity with less reward than predicted (negative prediction error). The dopamine signal increases nonlinearly with reward value and codes formal economic utility. Drugs of addiction generate, hijack, and amplify the dopamine reward signal and induce exaggerated, uncontrolled dopamine effects on neuronal plasticity. The striatum, amygdala, and frontal cortex also show reward prediction error coding, but only in subpopulations of neurons. Thus, the important concept of reward prediction errors is implemented in neuronal hardware.