The paper introduces Bayesian Kernel Machine Regression (BKMR) as a novel approach to estimate the health effects of multi-pollutant mixtures, addressing the limitations of existing methods that often focus on single agents or simple two-way interaction models. BKMR models the health outcome as a smooth function of the mixture components using a kernel function, allowing for flexible and non-linear exposure-response relationships. The method incorporates variable selection to identify important mixture components and accounts for the correlated structure of the mixture through a hierarchical variable selection approach. Simulation studies demonstrate the effectiveness of BKMR in estimating exposure-response functions and identifying key mixture components. The method is applied to two real-world datasets: an epidemiology study on metal mixtures and psychomotor development in Bangladesh, and a toxicology study on air pollution mixtures and hemodynamics. The results highlight BKMR's ability to handle complex exposure-response functions and identify important mixture components, even in the presence of highly correlated pollutants.The paper introduces Bayesian Kernel Machine Regression (BKMR) as a novel approach to estimate the health effects of multi-pollutant mixtures, addressing the limitations of existing methods that often focus on single agents or simple two-way interaction models. BKMR models the health outcome as a smooth function of the mixture components using a kernel function, allowing for flexible and non-linear exposure-response relationships. The method incorporates variable selection to identify important mixture components and accounts for the correlated structure of the mixture through a hierarchical variable selection approach. Simulation studies demonstrate the effectiveness of BKMR in estimating exposure-response functions and identifying key mixture components. The method is applied to two real-world datasets: an epidemiology study on metal mixtures and psychomotor development in Bangladesh, and a toxicology study on air pollution mixtures and hemodynamics. The results highlight BKMR's ability to handle complex exposure-response functions and identify important mixture components, even in the presence of highly correlated pollutants.