An apparatus for cleansing wounds in which irrigant fluid from a reservoir connected to a conformable wound dressing (2,41) and wound exudate from the dressing are recirculated by a device for moving fluid through a flow path which passes through the dressing (2,41) and a means for fluid cleansing and back to the dressing. The cleansing means (which may be a single-phase, e.g. micro-filtration, system or a two-phase, e.g. dialytic system) removes materials deleterious to wound healing, and the cleansed fluid, still containing materials that are beneficial in promoting wound healing, is returned to the wound bed. The present invention relates to the conformable wound dressing comprising a wound filler.