The movement of water beneath ice sheets exerts an important, yet poorly understood, control on how ice masses respond to climatic warming. However, the subglacial realm of ice sheets is one of the most inaccessible environments on Earth. Consequently, little is known about the processes that operate beneath today’s ice masses — and how these will evolve in the future. Subglacial landforms present in formerly-glaciated regions provide comparatively accessible records of glacial erosion, deposition, and sediment transport beneath ice sheets that have undergone deglaciation. This thesis investigates the potential of these landforms to reconstruct the flow of water beneath past ice sheets as analogues for how contemporary ice masses will evolve in a warming climate. A combination of geophysical approaches, including multibeam-bathymetric surveys, high-resolution 3D seismic-reflection data, conventional 3D seismic-reflection data, and geotechnical information from boreholes, is used to investigate the flow of water beneath ice sheets which covered western Europe and more expansive regions of the Antarctic continental shelf in the past. These data are first used to constrain the routing and fluxes of subglacial water beneath the retreating West Antarctic Ice Sheet. The impact of subglacial water flow on ice-sheet dynamics during deglaciation is then examined by imaging the internal structures of ancient channels incised by meltwater — tunnel valleys — in the North Sea. The unprecedented detail provided by the high-resolution 3D seismic-reflection data provides links between ice-sheet dynamics and subglacial meltwater flow during deglaciation. A numerical modelling approach constrains these linkages further by estimating the time that the meltwater channels take to form beneath deglaciating ice sheets. Finally, the sedimentation patterns resulting from subglacial water flow and other glacially-influenced processes during deglaciation are examined. Greater coverage of geophysical data on formerly glaciated continental margins, combined with chronological constraints from shallow drilling, will improve understanding of the hydrological systems and dynamics of former and contemporary ice sheets.