In the cold regions of the Earth, a continuous cover of permafrost characterizes the nonglaciated parts of the landscape. The permafrost layer separates hydrological processes into the near-surface and deep (subpermafrost) hydrological systems. Together with glaciers and ice sheets, the permafrost seals the deep groundwater system and solutes such as greenhouse gases produced in the deep subsurface. The subject of this PhD thesis is groundwater springs in continuous permafrost regions that are found above perennially unfrozen zones of the ground. These so-called talik springs form exceptional links for subpermafrost groundwater and solutes to reach the surface and atmosphere. Since they are most often located in lowlying Arctic valleys, such valleys served as the field areas of the PhD study. The four research papers included in this PhD thesis address some of the unresolved questions about the driving mechanisms behind talik springs and the landscape features that favor their formation. The first two research papers were motivated by an apparent lack of recharge sources to subpermafrost groundwater systems in some of the areas with talik springs. In Paper I, a conceptual model for talik springs driven by millennial-scale permafrost aggradation was developed in response to this apparent hydrological imbalance. The principal idea is that the expansion of water upon freezing can generate the sufficient hydraulic pressures to drive groundwater flow and talik spring discharge. The conceptual model was investigated through numerical modelling experiments in Papers I and II. The modelling experiments in Paper I used a sequential modelling scheme with separate simulations of heat transfer and groundwater flow and were based on field observations from Adventdalen, Svalbard. With the results from this first modelling study, we show that the proposed conceptual model does indeed represent a feasible mechanism for driving talik springs. In Paper II, a numerical model with increased process complexity was applied to conceptual valley geometries to quantify the likely magnitude and temporal ranges of the proposed conceptual model. Based on the findings of the second modelling study, we conclude that basal permafrost aggradation can explain talik spring outflow with up to a few liters per second and over millennial timescales after surface cooling has ceased. Previously, explanations offered for the locations of talik spring have focused on factors like hydraulically conductive geological units and faults. However, on Svalbard, several talik spring are found along valley margins and seemingly without these controlling factors. In Paper III, electrical resistivity tomography was used to investigate the geological setting surrounding one such talik spring. The results revealed that the talik spring is located exactly at the transition from low-permeable glacio-marine and fluvial sediments to consolidated and heavily fractured sedimentary strata in the shallow late Weichselian landscape relief. We suggest that this landscape relief could represent a previously unrecognized aquifer system. Paper IV describes the discovery of talik spring icings in West Greenland's Isortoq Valley. The icings are distributed with greater frequency towards the Greenland ice sheet (GIS) at the valley head but occur throughout the ~100-km-long valley. Three of the talik springs were sampled, and their geochemistry pointed to long contact with groundwater reservoir sediments. We suggest that the talik springs are expressions of a subpermafrost groundwater system that perennially routes meltwater produced at the base of GIS deep beneath the valley floor of Isortoq Valley. Arctic valleys deserve further attention as possible locations for surface discharge of deep groundwater and greenhouse gases, and as possible pathways for subpermafrost meltwater routing from ice sheets.