In ERP studies, the comparison of topographies (multichannel measurements) or whole spatiotemporal data matrices (multichannel time series of measurements), the classical statistical tests very often cannot be used. It is argued that, for these comparisons, randomization tests are an excellent alternative. It is also argued that the randomization test is superior to another resampling method, the bootstrap, because exact probability statements (e.g., p values) can be made. A review is given of the literature on randomization tests designed for electrophysiological data. New randomization tests are presented and applied to two data sets, one coming from a psychopharmacological experiment and the other from an ERP experiment in visual word recognition.