The hydrologic and geologic conditions beneath ice sheets play an important role in governing ice sheet behavior and determining their vulnerability to climate change. However, these subglacial conditions are challenging to resolve at the scale and resolution required to capture critical basal processes. This challenge can be addressed with the help of innovative geophysical, geostatistical, and computational methods, which provide avenues for imaging the ice/bed interface and assimilating geophysical observations from different spatial scales and resolutions. These approaches produce novel insights into the nature of the subglacial landscape and the dynamic behavior of our ice sheets.