This chapter shows how to extend the power of expected value analysis by introducing a more comprehensive approach to assigning values to outcomes. It shows how to assign measures to outcomes that capture both risk attitudes as well as the multidimensionality found in most medical decision problems. The fundamental approach of utility analysis is to determine a measure for each outcome, called the outcome utility, so that the alternative with the highest expected utility is the alternative most preferred by the decision maker. The chapter starts with a formal approach to assessing a decision maker's outcome utilities. It presents alternative approaches to determining a decision maker's outcome utilities, each based on simplifying assumptions about the decision maker's preferences. It also shows how to incorporate risk attitudes into the comparison of gambles based on the exponential survival model.