For many large-scale nonlinear inverse problems, Monte Carlo methods provide the only practical method of quantifying uncertainty. Ensemble-based methods such as the ensemble Kalman filter and ensemble smoothers have found increasing application in data assimilation systems for weather prediction, oceanography, and subsurface flow. In this talk, I will describe the methods in general, their connection with Gauss-Newton minimization methods and the approach to sampling. The methodology will be illustrated with several fairly large-scale examples from subsurface flow.