In a wide variety of domains, including weather and climate prediction, materials science, etc., computational scientists can now make impressively successful predictions using dynamical models. This success has sharpened concern about multiple sources of uncertainty. Every model is inexact in multiple respects; even the best data has errors; discretization introduces additional error. Can we assess and combine these uncertainties well enough gain a useful sense of the precision of a model's predictions? Can this help us combine divergent predictions from competing models? These questions have recently been addressed using Bayesian and Dempster-Shafer methods.