This article reviews the range of flows that may be created within thin cylindrical or annular cavities due to the rotation of one of the confining disks. At low Reynolds numbers, the rotation gives rise to an axisymmetric, radially outward motion near the rotor with a return flow along the stationary disk. As the Reynolds number is raised, this base flow gives way to a shear flow populated by discrete vortices, whether of cylindrical or spiral form, near both the rotating and stationary disks. At Reynolds numbers high enough for turbulent flow to occur, in the twentieth century both experimental and computational studies treated the flow as axisymmetric and steady. Recent research has shown, however, that complex organized structures also persist in the turbulent regime.