Described, in certain aspects, are medical devices that can be used to anchor graft materials to bodily structures. These devices comprise an implantable graft structure and tissue ingrowth material. This implantable graft structure is comprised of a body of persistent material having a first face and one or more openings defined therein, wherein the persistent material body first face is configured for opposing a bodily structure wall upon implantation. This tissue ingrowth material is positioned at the one or more persistent material body openings, and is configured for receiving tissue ingrowth from the bodily structure wall effective to anchor the graft structure to the bodily structure wall. The invention also provides methods utilizing these and other inventive medical devices, for example, to anchor graft materials to vascular vessel walls and/or other bodily structures.