Challenges arise in researching health effects associated with chemical mixtures. Several methods have recently been proposed for estimating the association between health outcomes and exposure to chemical mixtures, but a formal simulation study comparing broad-ranging methods is lacking. We select five recently developed methods and evaluate their performance in estimating the exposure-response function, identifying active mixture components, and identifying interactions in a simulation study. Bayesian kernel machine regression (BKMR) and nonparametric Bayes shrinkage (NPB) were top-performing methods in our simulation study. BKMR and NPB outperformed other contemporary methods and traditional linear models in estimating the exposure-response function and identifying active mixture components. BKMR and NPB produced similar results in a data analysis of the effects of multipollutant exposure on lung function in children with asthma.