The Earth’s cryosphere is changing rapidly, with global impacts. High Mountain Asia is experiencing warmer temperatures, with corresponding changes in glacier melt rates and precipitation patterns, which have significant implications for water resources as well as changes in patterns of geophysical hazards such as glacial lake outburst floods and surging glaciers. Subglacial hydrology (water drainage beneath glaciers) is an important piece of the glacier system, as the configuration of drainage and water pressure at the bed influences how quickly a glacier slides and modulates the timing and magnitude of glacial water discharge. The subglacial environment, however, is difficult to access for direct observations. Mathematical models provide a view into this hidden world, based on physical processes that allow us to simulate the evolution of water distribution and pathways, pressure, and ice velocity. I will present an overview of glacier hydrology and the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model, coupled with the Ice-sheet and Sea-level System Model (ISSM), with example applications to understand the physical processes driving the behavior of tidewater glaciers in Greenland, surging glaciers in the Karakoram, and non-surging Himalayan glaciers that display seasonal velocity variations. Accurate physics-based modeling depends on remotely sensed datasets, both for estimating surface melt and for validation using ice surface velocity and/or subglacial discharge imagery.