Yield stress liquids respond as elastic or viscoelastic solids prior to yielding, and they flow as viscous or viscoelastic liquids after yielding. Classical descriptions of yield stress liquids assume that yielding is a reversible process that occurs at an invariant surface in stress space, and certain general conclusions regarding flow structure and symmetries in the yielded regime follow. This description is inadequate to describe real fluids, however, probably because of a “thixotropic” response caused by disruption of the microstructure following the initiation of flow. This talk reviews yield-stress liquid behavior and ideas about incorporating microstructural response into continuum descriptions.