EEG and MEG measure brain electrical activity indirectly from outside the head, where each sensor measures a superposition of activity from the entire brain/cortex rather than only from its closest sourrounding. This limits the signal-to-noise ratio (SNR) of the measurements and prohibits the straightforward localization of the underlying brain activity. To perform localization, the physical mapping from brain electrical activity to EEG potentials/MEG magnetic fields has to be reversed, which is only possible using prior knowledge on the properties of the sources. A different approach to recovering EEG/MEG source activity is statistical source separation. Here, the data are factorized into source time series (components) and their corresponding static EEG potential/MEG field maps (patterns) based on assumptions such as mutual independence or class discriminability of the source time series. Although no physical model is employed in source separation methods, each component can be localized in a subsequent step. We will review established inverse source reconstruction and source separation algorithms employing various assumptions on the number of active sources, the spatial structure and the temporal dynamics of the source activity.