The flow of yield-stress liquids has been studied for nearly one hundred years, but major conceptual issues remain.  Yield-stress liquids respond as elastic or viscoelastic solids prior to yielding, and they flow as viscous or viscoelastic liquids after yielding.  The primary unresolved issue, at least from a simulation perspective, appears to be the description of the mechanics of the yielding phenomenon itself.  Classical descriptions of yield stress fluids 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 sometimes inadequate to describe real fluids, however, where a thixotropic response caused by disruption of the microstructure following the initiation of flow may result in dissipative motion at stresses below the nominal yield stress;.