Most large and complex physical systems are studied by mathematical models, implemented as high dimensional computer simulators. While all such cases differ in physical description, each analysis of a physical system based on a computer simulator involves the same underlying sources of uncertainty. These sources are defined and described below. In addition, there is a growing field of study which aims to quantify and synthesize all of the uncertainties involved in relating models to physical systems, within the framework of Bayesian statistics, and to use the resultant uncertainty specification to address problems of forecasting and decision making based on the application of these methods. We present an overview of the current status and future challenges in this emerging methodology, illustrating with examples drawn from current areas of application including: asset management for oil reservoirs, galaxy modeling, and rapid climate change.