The previous chapter discussed data assimilation for the case in which the variables have known Gaussian distributions. However, in atmospheric and oceanic data assimilation, the distributions are neither Gaussian nor known, and the large number of state variables creates numerical challenges. This chapter discusses a class of algorithms, called Ensemble Square Root Filters, for performing data assimilation with high-dimensional, nonlinear systems. The basic idea is to use a collection of forecasts (called an ensemble) to estimate the statistics of the background distribution. In addition, observational information is incorporated by adjusting individual ensemble members (i.e., forecasts) rather than computing an entire distribution. This chapter discusses three standard filters: the Ensemble Transform Kalman Filter (ETKF), the Ensemble Square Root Filter (EnSRF), and the Ensemble Adjustment Kalman Filter (EAKF). However, ensemble filters often experience filter divergence, in which the analysis no longer tracks the truth. This chapter discusses standard approaches to mitigating filter divergence, namely covariance inflation and covariance localization.