Categorization retains its key importance in research on human cognition. It is an intellectual area where all disciplines devoted to human cognition – psychology, philosophy, anthropology, and linguistics – intersect. In language, categorization is not only a central part of lexical structure but is also salient in systems of nominal classification, notably gender and classifiers. Recent years have seen great progress in the description and analysis of nominal classification systems, so that we are now in a position to offer an account of such systems which brings cognition and typology together, providing the essential parameters for the calibration of experiments for investigating cognition. To this end, we establish the extremes of nominal classification systems, from the surprisingly simple to the surprisingly complex. We analyse the two essential components of nominal classification systems: (i) assignment, i.e. the principles (semantic or formal) which govern category assignment and (ii) exponence, i.e. the morphological means by which systems of nominal classification are expressed. We discuss extreme configurations of assignment and exponence in individual languages and extreme multiple pairings of assignment and exponence in languages with two or even more concurrent classification systems.