AbstractWe review the use of Bayesian model averaging in astrophysics. We first introduce the statistical basis of Bayesian model selection and model averaging. We discuss methods to calculate the model‐averaged posteriors, including Markov chain Monte Carlo (MCMC), nested sampling, population Monte Carlo, and reversible jump MCMC (RJMCMC). We then review some applications of Bayesian model averaging in astrophysics, including measurements of the dark energy and primordial power spectrum parameters in cosmology, cluster weak lensing, and Sunyaev–Zel'dovich effect data, estimating distances to Cepheids and classifying variable stars. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 6: 3–14, 2013