Collapsible structures are provided that have one or more support frames, each having a foldable frame member that has a folded and an unfolded orientation, with the frame member defining a periphery for the support frame. Where more than one support frame is provided, the support frames can be hingedly coupled to each other. The frame member(s) can be used, for example, to support panel pieces, objects and coverings, among others. In some embodiments, one or more objects can be coupled to and supported by the support frame(s). In other embodiments, a covering may be placed over the support frame(s).