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Abstract Most theories of glacier movement and subglacial erosion have assumed that glaciers rest on rigid bedrock surfaces. Whilst this is probably correct for much of the bed area of most modern glaciers, deformable sediments do occur beneath them and formed a substantial area of the beds of large ice sheets during glacial periods. Observations and theories are presented and reviewed about the processes of glacier erosion of rock and unlithified sediment beds both when they are frozen and unfrozen. Erosional bedrock landforms, such as roches moutonnées , indicate two principal subglacial erosional processes, plucking and abrasion. Where supraglacially derived debris is unimportant, plucking provides the tools which abrade the bed, and must be a quantitatively more important process than abrasion, though more localized. Where plucking is suppressed, erosion rates must be slow. Subglacial measurements of abrasion rates beneath a temperate glacier are used to test an earlier abrasional theory (Boulton, [ C 1974]). The form of the predicted abrasion-rate curve for changing ice velocity and pressure is verified. This theory successfully simulates two-dimensional erosional bedforms. Subglacial observations demonstrate how flow basal ice around the flanks of bedrock obstacles causes streaming of debris to occur. It is suggested that this streaming process is primarily responsible for the longitudinally lineated form of large-scale surfaces typical of glacially eroded bedrock. Plucking and abrasion also occur beneath cold ice, though at slow rates, and are probably restricted to places where the ice thickness is small. Where the glacier bed is composed of unlithified sediment, subglacial measurements show that deformation can produce very large discharges of subglacial material, which makes this a potential agent of very rapid subglacial landform production. The heterogeneity of subglacial sediment leads to spatially variable rates of deformation, and it is suggested that relatively stronger parts of the sediment body may form the nuclei for drumlin and mega-flute formation. Whereas unlithified unfrozen sediment deforms beneath the glacier rather than being incorporated within it, ice-cemented subglacial sediments can behave like bedrock, because of their relative rigidity, and are readily plucked and incorporated englacially. They may also deform beneath the glacier.