The flow properties of concentrated polymer dispersions which exhibit extreme shear thickening have been investigated in steady and transient shearing flows using various types of rheometers. A phenomenological characterization based on few fluid parameters is proposed and pertinent test modes for their determination are discussed. The dispersions consist of monodisperse, electrostatically stabilized, solid spherical particles (diameter<0.5 μm) dispersed in glycols. They show a reversible steplike viscosity transition of nearly three powers of ten when an apparent critical shear rate γ̇cis exceeded. This jump from a low to a high viscosity state shows typical features of a shear‐rate‐induced phase transition, including hysteresis and the existence of a metastable low viscosity state above γ̇c. The viscosity step can be traced continuously by using stress controlled rheometers. Pronounced fluctuations of the rate of deformation with time are observed at the critical shear rate. The apparent critical shear rate depends on the rheometer geometry. Its change with the gap width in Couette flow and with the radius of circular dies can be interpreted by taking into account a true critical shear rate γ̇0and a wall slip velocityvs. Periodic switching to the high viscosity state in oscillatory shear only occurs if both a critical rate amplitude and a critical shear amplitude are reached during the cycle. Applications of these dispersions for simple speed controlling or selectively damping mechanical elements are briefly introduced.