Introduction: This article discusses expected utility theory as a normative theory - that is, a theory of how people should make decisions. In classical economics, expected utility theory is often used as a descriptive theory - that is, a theory of how people do make decisions - or as a predictive theory - that is, a theory that, while it may not accurately model the psychological mechanisms of decision-making, correctly predicts people's choices. Expected utility theory makes faulty predictions about people's decisions in many real-life choice situations (see Kahneman & Tversky 1982); however, this does not settle whether people should make decisions on the basis of expected utility considerations. The expected utility of an act is a weighted average of the utilities of each of its possible outcomes, where the utility of an outcome measures the extent to which that outcome is preferred, or preferable, to the alternatives. The utility of each outcome is weighted according to the probability that the act will lead to that outcome. Section 1 fleshes out this basic definition of expected utility in more rigorous terms, and discusses its relationship to choice. Section 2 discusses two types of arguments for expected utility theory: representation theorems, and long-run statistical arguments. Section 3 considers objections to expected utility theory; section 4 discusses its applications in philosophy of religion, economics, ethics, and epistemology.