Regression modeling sits at the core of most efforts in environmental epidemiology where the goal is to investigate the association between exposures of interest and a given health outcome. This chapter presents the challenges of applying standard regression approaches for assessing mixture-health associations, introducing the key concepts of data overfitting and collinearity. Next, the framework of penalized regression is introduced, discussing the application and interpretation of Ridge, LASSO, and Elastic Net regression and their advantages and limitations in the context of environmental mixtures.