The pore-water signal left behind by a glacier overriding a porous medium is considered. Important processes are infiltration, tracer diffusion, radio-active decay, penetration of freezing fronts and erosion and deposition. Our knowledge of the basal hydrology of glaciers is so incomplete that we are not able to determine on theoretical grounds how much water should infiltrate the ground; water can drain through aquifers to the margin, through the aquifer to sub-glacial channels, or entirely at the glacier bed. Infiltration could be negligible or affect the whole depth of the aquifer. Diffusion is limited by the tortuosity parameter, which as yet is poorly explained by theory. Diffusion over 20,000 years may only affect a depth of 10 m, which means that the relevant areas are readily accessible by cores but are likely to have been disturbed by surface effects. The influence of sedimentation and unstable tracers is discernible but sometimes difficult to distinguish from the effects of the glaciation history. First steps in an observation programme should be the establishment of the typical depth to which marine sediments are affected. This will constrain the basal hydrology, and reduce the number of possible scenarios.