Water-rock interactions within the seafloor are responsible for significant energy and solute fluxes between basaltic oceanic crust and the overlying ocean. Permeability is the primary hydrologic property controlling the form, intensity, and duration of seafloor fluid circulation, but after several decades of characterizing shallow oceanic basement, we are still learning how permeability is created and distributed and how it changes as the crust ages. Core-scale measurements of basaltic oceanic crust yield permeabilities that are quite low (generally 10-22 to 10-17 m2), while in situ measurements in boreholes suggest an overlapping range of values extending several orders of magnitude higher (10-18 to 10-13 m2). Additional indirect estimates include calculations made from borehole temperature and flow meter logs (10-16 to 10-11 m2), numerical models of coupled heat and fluid flow at the ridge crest and within ridge flanks (10-16 to 10-9 m2), and several other methods. Qualitative indications of permeability within the basaltic oceanic crust come from an improved understanding of crustal stratigraphy and patterns of alteration and tectonic modification seen in ophiolites, seafloor samples and boreholes. Difficulties in reconciling the wide range of estimated permeabilities arise from differences in experimental scale and critical assumptions regarding the nature and distribution of fluid flow. Many observations and experimental and modeling results are consistent with permeability varying with depth into basement and with primary basement lithology. Permeability also seems to be highly heterogeneous and anisotropic throughout much of the basaltic crust, as within crystalline rocks in general. A series of focused experiments is required to resolve permeability in shallow oceanic basement and to directly couple upper crustal hydrogeology to magmatic, tectonic, and geochemical crustal evolution. ¿ 1998 American Geophysical Union