Linear regression can be extended in a number of ways to fit various modeling needs. Regularized regression penalizes the magnitude of the regression coefficients to avoid overfitting, which is particularly helpful for models using a large number of predictors. Bayesian regression places a prior distribution on the regression coefficients in order to reconcile existing beliefs about these parameters with information gained from new data. Finally, generalized linear models (GLMs) expand on ordinary linear regression by changing the assumed error structure and allowing for the expected value of the target variable to be a nonlinear function of the predictors. These extensions are described, derived, and demonstrated in detail this chapter.