Abstract The response of coastal aquifer systems to global sea-level rise, the presence of permafrost and glaciation has been analysed using analytical and numerical models. The hydraulic connectivity between confined coastal aquifers and the sea largely controls their response to global sea-level rise. Open aquifer systems have direct hydraulic contact with the sea where they sub crop along the continental slope and base-level history for the aquifer is defined by sea-level history. In these systems, hydraulic heads equilibrate quickly to sea-level change at rates controlled by the aquifer hydraulic diffusivity. Interface movement lags behind the equilibration of the hydraulic heads and is controlled largely by the rate at which freshwater can be flushed from the aquifer through overlying semi-confining units. Interface movement occurs over time periods of tens of thousands of years. In contrast, closed aquifer systems lack direct hydraulic connectivity with the sea, which is controlled by the thickness and permeability of overlying semi-confining layers. During the Late Pleistocene–Early Holocene the base-level history for closed aquifer systems underlying the North Sea Basin was defined by the location of rivers and lakes in areas that are now offshore. These aquifers became coastal aquifers during the Holocene when rivers and lakes were inundated by rising sea levels. Salinization of closed aquifer systems may occur due to the downward diffusion of salts through overlying semiconfining layers in the presence of upward freshwater seepage. Aquifers overridden by glaciers respond in a manner that is largely controlled by aquifer transmissivity and geometry. The presence of permafrost inhibits recharge resulting in lower hydraulic heads and a reduction in aquifer fluxes.