Computational models of complex physical systems are fraught with uncertainties. These include uncertainties in initial or boundary conditions, uncertainties in model parameters and/or the experimental data used to calibrate them and uncertainties arising from imperfections in the models used in the simulations. Mathematical models of these uncertainties and their affects on the quantities the models are intended to be predicted (the quantities of interest or QoI's) are needed. It is also necessary to assess the ability of the models to represent both the physics of the phenomena being predicted and the associated uncertainties, and in particular the ability to predict the QoI's and their uncertainty. However, in the usual situation, the QoI's are not accessible for observation, since otherwise, no computational prediction would be necessary. We thus must use available or attainable observational data (and estimates of their uncertainty) to calibrate the models and evaluate the ability of the models to predict the unobserved QoI's. In this talk, a Bayesian framework for these calibration and validation processes is proposed and applied to several examples. However, a number of conceptual and practical challenges to applying these ideas in complex systems remain, and will be discussed along with possible approaches to address these problems.