Collapsible structures are provided having at least one lower panel, each panel having a foldable frame member having a folded and an unfolded orientation, with a fabric material substantially covering the frame member to form the panel when the frame member is in the unfolded orientation. The fabric assumes the unfolded orientation of its frame member, and each panel further includes a first side, a second side, a bottom side and a top side. The first side of one panel is coupled to the second side of an adjacent panel. The collapsible structure according to the present invention further includes an upper panel having a bottom side coupled to the top side of one of the lower panels. In other embodiments, at least two upper panels are provided, with the upper panels provided above the lower panels. The respective panels can be coupled to each other using stitching and/or detachable connectors, or by crossing the frame members of the panels at adjacent left, right, top or bottom sides.