Regression estimates functional dependencies between features. Linear regression models can be efficiently computed from covariances but are restricted to linear dependencies. Substitution allows to identify specific types of nonlinear dependencies by linear regression. Robust regression finds models that are robust against outliers. A popular class of nonlinear regression methods are universal approximators. We present two well-known examples for universal approximators from the field of artificial neural networks: the multilayer perceptron and radial basis function networks. Universal approximators can realize arbitrarily small training errors, but cross-validation is required to find models with low validation errors that generalize well on other data sets. Feature selection allows us to include only relevant features in regression models leading to more accurate models.