Accretionary prisms are wedges of saturated sediment that are subject to intense deformation as a result of lithosphere convergence. Compressive stress and rapid burial of the accreted deposits result in sediment compaction and mineral dehydration. These latter processes, in conjunction with fermentation or thermal maturation of entrained organic matter, yield hydrocarbon-bearing pore fluids that are expelled from the prism. Regional fluxes of heat and a number of dissolved chemical species, most notably carbon, are controlled by the advective expulsion of the pore waters. Numerical modeling, observation and monitoring of flow patterns and rates, and recent in situ hydrogeological tests quantify the conditions that control rates of fluid flow. Dispersed, intergranular flow (10-8 to 10-11 m/s), controlled by the vertical permeability of the prism (10-14 to 10-20 m2), is limited by low-permeability lithologies and seems not to vary much from margin to margin. Focused flow (10-1 to 10-8 m/s) above the d¿collement is controlled by fault zones or sedimentary intrusions (diapiric structures). At low-fluid pressures, fault zone permeability may be similar to that of adjacent wall rock, but as fluid pressure increases from hydrostatic (λ*=0) to near lithostatic levels (λ*≈1.0), fault zones dilate, and (fracture) permeability increases by 2--4 orders of magnitude (10-10 to 101-16 m2). Similarly, mud volcanoes and diapirs provide high-permeability fluid conduits to the sediment-water interface. As a result, faults and intrusions become primary flow paths and support surface vents at which syntectonic deposits (carbonate and gas hydrates) accumulate and chemosynthetic organisms cluster. Models of thermal and chemical anomalies and epigenetic deposits indicate that flow is temporally variable. That conclusion has been quantified by extended (1--10 months) seafloor and borehole experiments that measured temperature anomalies associated with flow events. On the Cascadia prism, flow (estimated velocity ~3¿10-5 m/s; 950 m/yr), confined to a thrust fault that cuts upward through the prism, has brought thermogenic hydrocarbons from depths >1.5 km to the surface within the last 400 years. ¿ 1998 American Geophysical Union