The range of scales and complexity in multiscale, multiphysics systems means that obtaining accurate numerical simulations is extremely difficult. Consequently, there is an increasing — even strident — demand for quantification of error and uncertainty in model predictions. I will describe a powerful general approach for computing accurate estimates and the use of such estimates to mitigate the effects of error, e.g. through adaptive mesh refinement. I will explain the approach in the context of three interesting applications.