The mechanisms through which environmental mixtures affect human physiology often include complex interactions and non-linearities. The first section of this chapter describes the analytical tools that can be used to incorporate non-linear and non-additive effects in regression modeling and describes the potential threat of overfitting. This problem can be addressed through the application of nonparametric approaches that do not make assumptions of linearity and additivity. Specifically, the chapter introduces the framework of Bayesian Kernel Machine Regression (BKMR) and Generalized Additive Models (GAMs) as flexible tools for the assessment of mixture-health associations in complex settings, discussing their properties, implementation, and interpretation. Finally, the chapter provides a general overview of the application of machine learning for environmental mixtures, discussing those situations where these assumptions-free approaches could be of relevance.