The quantitative analysis of the electroencephalogram (EEG) relies heavily on methods of time series analysis. A quantitative approach seems indispensable for research (be it clinical or basic neurophysical research), but it can also be a useful information for purely clinical purposes. Apart from the ongoing spontaneous EEG, evoked potentials (EPs) also play an important role. They can be elicited by simple sensory stimuli or more complex stimuli. Their analysis requires methods which are different from those for the spontaneous EEG. Those methods operate usually in the time domain and offer many challenging problems to statisticians. Methods for analysing the spontaneous EEG usually work in the frequency domain in terms of spectra and coherences. Biomedical engineers who take care of the equipment are usually also trained in time series analysis. Thus, they have contributed much more to methodological progress for analysing EEGs and EPs, compared with statisticians. However, the availability of a sample of subjects, and the associated problems in modelling followed by an inferential analysis could make a larger influence from the statistical side quite profitable. This paper tries to give an overview of a fascinating area. In doing so we treat more extensively problems with some statistical appeal. This leads inevitably to some overlap with our own work.