Groundwater processes are often overlooked in permafrost environments, but subsurface storage and routing can strongly influence water and biogeochemical cycling in northern catchments. Groundwater flow in permafrost regions is controlled by the temporal and spatial distribution of frozen ground, causing the hydrogeologic framework to be temperature-dependent. Most flow occurs in geologic units above the permafrost table (supra-permafrost aquifers) or below the permafrost base (sub-permafrost aquifers). In the context of climate change, thawing permafrost is altering groundwater flowpaths and thereby inducing positive trends in river baseflow in many discontinuous permafrost basins. Activated groundwater systems can provide new conduits for flushing Arctic basins and transporting nutrients to basin outlets. The thermal and hydraulic physics that govern groundwater flow in permafrost regions are strongly coupled and more complex than those in non-permafrost settings. Recent research activity in permafrost hydrogeological modeling has resulted in several mainstream groundwater models (e.g., SUTRA, FEFLOW, HYDRUS) offering users advanced capabilities for simulating processes in aquifers that experience dynamic freeze-thaw. This chapter relies on field examples to review key processes and conditions that control groundwater dynamics in permafrost settings and presents an up-to-date synthesis of the mathematical representation of heat transfer and groundwater flow in northern landscapes.