Direct or indirect measurements of fluid flow out of the toe of accretionary wedges have now been made in the Barbados, Central Oregon, Northern Cascadia and Nankai subduction zones. The steady-state local compaction model predicts velocities of fractions of a millimetre per year and total outflows from the toe of a few cubic metres per year per metre of length along strike of the subduction zone (m<sup>2</sup> a<sup>-1</sup>). Sea bottom measurements reveal channellized flows at velocities of hundreds of metres per year and total outflows from the toes of a few hundreds of square metres per year. Thermal arguments show in the Nankai area that all of this large surface flow cannot come from as deep as the decollement and that consequently a significant dilution by shallow sea water convection must be present. We propose that this convection is driven by the reduced density of less saline fluid of deep origin. Thus the outflow of water of deep origin may be only a few tens of square metres per year. We note, however, that there are indications in the Barbados area of massive flow of low salinity water at depth along the decollement. These flows imply the existence of large scale non-steady-state lateral transport and require the existence of sources of low salinity water. These might include the smectite-illite transformation and the fluid contained in the oceanic crust. However, these sources are limited and the possibility exist that other more important sources may be required such as long distance transport of fresh water from adjacent sedimentary basins and (or) recharge mechanisms such as the seismic pumping one.