Statistical decision rules map data into actions. Point estimators, inference procedures, and forecasting methods can be viewed as statistical decision rules. However, other types of rules are possible, such as rules for assigning individuals to treatments based on covariates, and methods for designing auctions. We discuss heuristics for constructing statistical decision rules, and survey results that characterize the properties of various classes of decision rules. Particular attention is paid to developing large-sample approximations to the distributions and associated risk properties of statistical decision rules.