Local regression models provide methods for fitting regression functions, or regression surfaces, to data. The chapter describes the specifications of a particular model determine the details of the method used to fit the model; the fitting method, which is called loess. It discusses the S functions and objects for local regression models by working through a number of examples. Our goal is to show how the data are analyzed in practice using S. This means we must discuss diagnostic methods. Thus, diagnostic checking is an essential part of the practice of fitting local regression models, and, as with all model building, omitting it results in demonstrated validity being replaced simply by hope. Thus, the fitting of local regression models involves making the following choices about the specification of properties of the errors and the regression surface. Properties are Gaussian or symmetric distribution; constant variance or a priori weights; locally linear or locally quadratic in numeric predictors; and neighborhood size.