There is an emerging consensus that higher plants synthesize cellulose microfibrils that initially comprise 18 chains. However, the mean number of chains per microfibril is usually greater than 18, sometimes much greater. Microfibrils from woody tissues of conifers, grasses and dicotyledonous plants, and from organs like cotton hairs, all differ in detailed structure and mean diameter. Diameters increase further when aggregated microfibrils are isolated. Because surface chains differ, the tensile properties of the cellulose may be augmented by increasing microfibril diameter. Association of microfibrils with anionic polysaccharides in primary cell walls and mucilages leads to mechanisms of disaggregation that may be relevant to the preparation of nanofibrillar cellulose products. For the preparation of nanocrystalline celluloses, the key issue is the nature and axial spacing of disordered domains at which axial scission can be initiated. These disordered domains do not, as has often been suggested, take the form of large blocks occupying much of the length of the microfibril. They are more likely to be located at chain ends or at places where the microfibril has been mechanically damaged, but their structure and the reasons for their sensitivity to acid hydrolysis need better characterization.This article is part of a discussion meeting issue 'New horizons for cellulose nanotechnology'.