The entry by Claeskens and Jansen (same volume) provides an overview of nonparametric estimation and describes the major classes of nonparametric regression methods in use today. In the current entry, we provide more details on two of these classes, kernel methods and spline methods. When applying these methods, the researcher is interested in estimating the relationship between one dependent variable, Y , and one or several covariates, X 1, …, X q .