Standard Bayesian inference is known to be sensitive to misspecification between the model and the data-generating mechanism, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for robust Bayesian inference under misspecification has proven to be a difficult challenge. An intriguing, easy-to-implement approach is to use bagging on the Bayesian posterior (“BayesBag”); that is, to use the average of posterior distributions conditioned on bootstrapped datasets. In this talk, I describe the statistical behavior of BayesBag, propose a model–data mismatch index for diagnosing model misspecification using BayesBag, and show empirical validation our BayesBag methodology on synthetic and real-world data. We find that in the presence of significant misspecification, BayesBag yields more reproducible inferences, has better predictive accuracy, and selects correct models more often than the standard Bayesian posterior; meanwhile, when the model is correctly specified, BayesBag produces superior or equally good results for parameter inference and prediction, while being slightly more conservative for model selection. Overall, our results demonstrate that BayesBag combines the attractive modeling features of standard Bayesian inference with the distributional robustness properties of frequentist methods.