We review the contributions to our understanding of the hydrogeology of the oceanic crust as gained by monitoring subseafloor temperatures and pressures in CORK (“Circulation Obviation Retrofit Kit”) sealed hole observatories that penetrate through marine sediments into igneous basement. CORKs were installed during 1991–2012 in 17 holes drilled by the Ocean Drilling Program and Integrated Ocean Drilling Programs in igneous oceanic crust (aged 0.4–24 Ma) in the thickly sedimented eastern Pacific Ocean and in the thinly sedimented north Atlantic Ocean. Results indicate that the igneous crust in all these settings is highly transmissive and supports vigorous lateral fluid flow and (or) convection beneath the sediment cover driven by very small horizontal pressure gradients. Inter-CORK experiments suggest that the horizontal permeability of the young oceanic basement at these sites may be anisotropic, with higher values in the direction parallel to the axis of spreading and tectonic fabric and lower values in a ridge-normal cross-strike direction. Tracer experiments applied to ridge-parallel flow suggest that only a small fraction of the crust is well connected. CORKs also record the response of subseafloor formation fluid pressures to seafloor tidal loading, and, once the tidal responses are filtered out, response to tectonic strain events. Interpretations based on these responses and original two-dimensional modelling of ridge-normal fluid circulation in the crust suggest a scale dependence of permeability of igneous oceanic crust (higher values at larger scales up to tens of km), although recent three-dimensional models suggest a more limited scale effect. CORKs have also provided important geochemical and microbiological results from the igneous oceanic crust, although they are not reviewed in this paper.