Abstract This chapter describes a family of statistical techniques called linear and non-linear regression that are commonly used in medical research. Regression is typically used to relate an outcome (or dependent variable or response) to one or more predictor variables (or independent variables or covariates). We examine several ways in which the standard linear model can be extended to accommodate non-linearity. These include non-linear transformation of predictors and outcomes within the standard linear model framework; generalized linear models, in which the mean of the outcome is modeled as a non-linear transformation of the standard linear function of regression parameters and predictors; and fully non-linear models, in which the mean of the outcome is modeled as a non-linear function of the regression parameters. We also briefly discuss several special topics, including causal models, models with measurement error in the predictors, and missing data problems.