Flow can induce reversible and irreversible structural changes in dispersions. The analysis of flow effects on microstructure and rheology remains one of the challenging problems in colloid science. The rheological manifestation of flow-induced structural changes is a variable viscosity. If the changes are reversible and time dependent, the effect is called thixotropy. The basic elements of this concept are reviewed here, including its definition and the relation with nonlinear viscoelasticity. The omnipresence of thixotropy is illustrated with a wide range of examples from natural and manmade colloidal systems. Its various rheological manifestations are reviewed as well as possible measurement procedures. The microstructural changes due to flow are quite complex and not fully understood. Existing models for thixotropic suspension rheology are categorized and evaluated.