In the attempts to localize electric sources in the brain on the basis of multichannel EEG and/or MEG measurements, distributed source estimation procedures have become of increasing interest. Several commercial software packages offer such localization programs and results using these methods are seen more and more frequently in the literature. It is crucial that the users understand the similarities and differences of these methods and that they become aware of the advantages and limitations that are inherent to each approach. This review provides this information from a theoretical as well as from a practical point of view. The theoretical part gives the algorithmic basis of the electromagnetic inverse problem and shows how the different a priori assumptions are formally integrated in these equations. The authors restrict this formalism to the linear inverse solutions i.e., those solutions in which the inversion procedure can be represented as a matrix applied to the data. It will be shown that their properties can be best characterized by their resolution kernels and that methods with optimal resolution matrices can be designed. The authors also discuss the important problem of regularization strategies that are used to minimize the influence of noise. Finally, a new kind of inverse solution, termed ELECTRA (for ELECTRical Analysis), is presented that is based on constraining the source model on the basis of the currents that can actually be measured by the scalp recorded EEG. The practical part of the review illustrates the localization procedures with different clinical data sets. Three aspects become important when working with real data: 1) Clinical data is usually far from ideal (limited number of electrodes, noise, etc.). The behavior of inverse procedures in such unfortunate situations has to be evaluated. 2) The selection of the time points or time periods of interest is crucial, especially in the analysis of spontaneous EEG. 3) Additional information coming from other modalities is usually available and can be incorporated. The authors are illustrating these important points in the case of interictal and ictal epileptiform activity. Spike averaging, frequency domain source localization, and temporal segmentation based on electric field topographies will be discussed. Finally, the technique of EEG-triggered functional magnetic resonance imaging (fMRI) will be illustrated, where EEG is recorded in the magnet and is used to synchronize fMRI acquisition with interictal events. The analysis of both functional data, i.e. the EEG in terms of three-dimensional source localization and the EEG-triggered fMRI, combines the advantages of the two techniques: the temporal resolution of the EEG and the spatial resolution of the fMRI.