Many soft materials, including microgels, dense colloidal emulsions, star polymers, dense packings of multilamellar vesicles, and textured morphologies of liquid crystals, share the basic 'glassy' features of structural disorder and metastability. These in turn give rise to several notable features in the low frequency shear rheology (deformation and flow properties) of these materials: in particular, the existence of a yield stress below which the material behaves like a solid, and above which it flows like a liquid. In the last decade, intense experimental activity has also revealed that these materials often display a phenomenon known as shear banding, in which the flow profile across the shear cell exhibits macroscopic bands of different viscosity. Two distinct classes of yield stress fluid have been identified: those in which the shear bands apparently persist permanently (for as long as the flow remains applied), and those in which banding arises only transiently during a process in which a steady flowing state is established out of an initial rest state (for example, in a shear startup or step stress experiment). Despite being technically transient, such bands may in practice persist for a very long time and so be mistaken for the true steady state response of the material in experimental practice. After surveying the motivating experimental data, we describe recent progress in addressing it theoretically, using the soft glassy rheology model and a simple fluidity model. We also briefly place these theoretical approaches in the context of others in the literature, including elasto-plastic models, shear transformation zone theories, and molecular dynamics simulations. We discuss finally some challenges that remain open to theory and experiment alike.
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