Collapsible structures include at least first and second panels, each panel having a foldable frame member that has a folded and an unfolded orientation, and a material covering portions of the frame member when the frame member is in the unfolded orientation. The first panel has a first retaining mechanism that defines an adjustment space, and the second panel has a second retaining mechanism that is movably received inside the adjustment space of the first retaining mechanism to couple the second panel to the first panel. The second retaining mechanism is movable within the adjustment space to allow the relative positions of the first and second panels to be adjusted. Other collapsible structures include at least first and second panels, each panel having a foldable frame member that has a folded and an unfolded orientation, and a material covering portions of the frame member when the frame member is in the unfolded orientation. A connector couples the first and second panels in a manner that allows the relative positions of the first and second panels to be adjusted.