Neuroeconomics combines methods and theories from neuroscience psychology, economics, and computer science in an effort to produce detailed computational and neurobiological accounts of the decision-making process that can serve as a common foundation for understanding human behavior across the natural and social sciences. Because neuroeconomics is a young discipline, a sufficiently sound structural model of how the brain makes choices is not yet available. However, the contours of such a computational model are beginning to arise; and, given the rapid progress, there is reason to be hopeful that the field will eventually put together a satisfactory structural model. This paper has two goals: First, we provide an overview of what has been learned about how the brain makes choices in two types of situations: simple choices among small numbers of familiar stimuli (like choosing between an apple or an orange), and more complex choices involving tradeoffs between immediate and future consequences (like eating a healthy apple or a less-healthy chocolate cake). Second, we show that, even at this early stage, insights with important implications for economics have already been gained.