Climate change is expected to reduce water security in arid mountain regions around the world. Vulnerable water supplies in semi-arid zones, such as the Dry Andes, are projected to be further stressed through changes in air temperature, precipitation patterns, sublimation, and evapotranspiration. Together with glacier recession this will negatively impact water availability. While glacier hydrology has been the focus of scientific research for a long time, relatively little is known about the hydrology of mountain permafrost. In contrast to glaciers, where ice is at the surface and directly affected by atmospheric conditions, the behaviour of permafrost and ground ice is more complex, as other factors, such as variable surficial sediments, vegetation cover, or shallow groundwater flow, influence heat transfer and time scales over which changes occur. The effects of permafrost on water flow paths have been studied in lowland areas, with limited research in the mountains. An understanding of how permafrost degradation and associated melt of ground ice (where present) contribute to streamflow in mountain regions is still lacking. Mountain permafrost, particularly rock glaciers, is often conceptualized as a (frozen) water reservoir; however, rates of permafrost ground ice melt and the contribution to water budgets are rarely considered. Additionally, ground ice and permafrost are not directly visible at the surface; hence, uncertainties related to their three-dimensional extent are orders of magnitude higher than those for glaciers. Ground ice volume within permafrost must always be approximated, further complicating estimations of its response to climate change. This review summarizes current understanding of mountain permafrost hydrology, discusses challenges and limitations, and provides suggestions for areas of future research, using the Dry Andes as a basis.