Slow feature analysis (SFA) is a biologically motivated algorithm for extracting slowly varying features from a quickly varying signal and has proven to be a powerful general-purpose preprocessing method for spatio-temporal data in brain modeling as well as technical applications. We have applied SFA to the learning of complex cell receptive fields, visual invariances for whole objects, and place cells in the hippocampus. On the technical side SFA can be used to extract slowly varying driving forces of dynamical systems and to perform nonlinear blind source separation. More recently we have developed methods to generalize SFA to supervised learning of data without explicit time structure but high dimensional input vectors, in particular for face processing. In an attempt to move beyond slowness we have developed algorithms that extract predictable rather than slowly varying features. However, on real-world data, SFA usually outperforms these new algorithms because of its simplicity and robustness.