The Bayesian paradigm provides a coherent approach for quantifying uncertainty given available data and prior information. Aspects of uncertainty that arise in practice include uncertainty regarding parameters within a model, the choice of model, and propagation of uncertainty in parameters and models for predictions. In this talk I will present Bayesian approaches for addressing model uncertainty given a collection of competing models including model averaging and ensemble methods that potentially use all available models and will highlight computational challenges that arise in implementation of the paradigm.