The literature on this subject stands currently at over 100 articles; this review seeks to present an overall picture of the subject, using the results of these articles. Concentrated suspensions of nonaggregating solid particles, if measured in the appropriate shear rate range, will always show (reversible) shear thickening. The actual nature of the shear thickening will depend on the parameters of the suspended phase: phase volume, particle size (distribution), particle shape, as well as those of the suspending phase (viscosity and the details of the deformation, i.e., shear or extensional flow, steady or transient, time and rate of deformation). The explanations offered for the phenomenon that are supported by independent physical measurements postulate that the increase in viscosity is due to the transition from a two‐dimensional layered arrangement of particles to a random three‐dimensional form. The transition rarely takes more than one decade of shear rate, but it can be over a much shorter range, making the increase quite dramatic. These factors of course depend strongly on the particle and fluid parameters. For a suspension of monodisperse spheres suspended in a low viscosity fluid (1–10 mPa⋅s), the onset of shear thickening is very dependent on the sphere diameter, approximately according to an inverse quadratic relationship, with the value for 10 μm spheres being about0.1 s−1in steady shear and so on. The severity of the shear thickening depends on the concentration, in proportion to some maximum packing fraction which is itself partly controlled by the form of the particle size distribution. The particle shape is also important. The extent of the phenomenon can be greatly reduced by either reducing the particle size, thus delaying the onset to higher shear rate, or by using a mixture of particle sizes. This latter procedure changes the onset condition, and reduces the severity by increasing the maximum packing fraction of the suspended material.