Abstract: Since the early 1970's, weather forecast models have been initialized using data assimilation algorithms based on approximations to the Kalman filter equations. The accuracy of the analyses produced by these schemes has steadily improved as these approximations have been relaxed. The most challenging part of implementing a full Kalman filter for high dimensional systems is accurately modelling the background-error covariance. Over the past decade, many operational centers have begun to use ensembles of short-range forecasts for this purpose. I will show how these ensemble-based estimates of the background-error covariance are used in operational data assimilation systems, with a particular emphasis on the hybrid ensemble-variational approach now used operationally in NOAA. The limitations of current systems will be discussed, as well as approaches currently under development for addressing them.