Shear deformation of sediments is widespread beneath glaciers. Sediment rheology and the structure of the subglacial drainage system control the deformational behaviour of sediments and the way in which they play a role in determining the dynamics of glaciers, the magnitude of subglacial erosion, the nature of till deposition and many geotechnical properties of glacial sediments which are of concern to engineers. It is suggested that a power law relating shear strain rate, shear stress and effective stress is the most useful general description of their continuum behaviour. Evidence is reviewed from laboratory and field experiments, from the structural properties of tills and from the large-scale patterns of till deposition by former ice sheets to suggest the principal modes of rheological behaviour for tills of different granulometries and to speculate on the interparticle processes which determine them.