The role of forecast error covariance in practical ensemble and variational data assimilation is described following algebraic and dynamical views. This is used to introduce a motivation for ensemble data assimilation. It is shown how a dynamically induced and anisotropic ensemble error covariance can benefit data assimilation, compared to climatological (static) and isotropic error covariance used in variational methods. In addition to the standard ensemble Kalman filter (EnKF), more practical square root EnKF equations are also presented. Direct transform ensemble methods are also introduced and their connection with both ensemble and variational methods described. Error covariance localization in terms of the Schur product, a standard component of any realistic ensemble-based data assimilation, is also introduced and discussed. Following that, hybrid data assimilation and in particular the ensemble-variational (EnVar) methods are introduced and presented in relation to pure ensemble and variational methods. As a particular example of hybrid methods the maximum likelihood ensemble filter (MLEF) is introduced.