A luggage system is disclosed comprising a plurality of interchangeable components. Each component has at least one perimeter attachment means which is mateable with a counterpart perimeter attachment means on an adjacent component, thereby making the various components releasably attachable and completely detachable. The possible components of the luggage system may be a luggage case, a spacing member, an enclosure piece, and/or carrying means to allow a traveler to build a variety of luggage pieces that suit the particular packing, organizing, and transporting needs of the traveler.