This chapter surveys the technical aspects of the self-protection problem in the expected utility model. Self-protection is a costly investment to reduce the probability of loss. Even in the simplest model with a binary risk of loss, the objective function is not necessarily concave in the level of self-protection, and deriving clean comparative statics has proven notoriously difficult. This chapter discusses the regularity of the self-protection problem, the trade-off between risk aversion and downside risk aversion, and the role of probability thresholds. It presents results about the decision to engage in self-protection (i.e., the extensive margin) and the optimal level of self-protection (i.e., the intensive margin). Recent intertemporal extensions to two periods are also discussed with a focus on the role of saving as a substitute for self-protection.