Delay discounting refers to the set of cognitive and neural processes that underlie our ability to value rewards or punishments that will be received after a time delay. People and other animals prefer to receive rewards sooner and to delay punishments, all else being equal. Cognitive neuroscience has identified a set of brain areas that are involved in delay discounting and has documented how interactions between these brain areas support intertemporal decision-making. We describe these advances and argue that cognitive neuroscience has successfully identified the brain network involved in delay discounting, enabling current research focused on how discounting is altered in disorders such as addiction and attention deficit hyperactivity disorder (ADHD). Future advances in our understanding of the neural mechanisms of delay discounting will benefit from methodological advances, such as the use of novel techniques for measuring dopamine release in humans.