The ensemble Kalman filter (EnKF) is a computational technique for approximate inference on the state vector in state-space models. It has been successfully used in many real-world data-assimilation problems with very high dimensions. However, the EnKF assumes the state-space model to be fully known and to be at least approximately linear and Gaussian. Here, we consider a broader class of hierarchical state-space models, which include two additional “layers”: The parameter layer allows handling of unknown parameters that cannot be easily included in the state vector, while the observation layer can be used to model non-Gaussian observations. We propose a general class of extended ensemble Kalman filters and smoothers for (approximate) Bayesian inference in our hierarchical state-space models. We highlight several interesting examples, such as a robust EnKF for heavy-tailed observations, and assimilation of rainfall amounts.