Collapsible indoor and outdoor containers having a collapsible wall section with shape-retaining characteristics are disclosed. In particular, collapsible coolers, fish bins, and wheeled vertical bins are provided. The collapsible wall section may include foldable tiers of a flexible material, each tier having at least one stable, relatively expanded position and at least one stable, relatively collapsed position; and an intervening, non-folding tier composed of a different, relatively stiff or rigid material. The coolers, fish bins, and wheeled vertical bins are each advantageously provided with a collapsible insert container that nests within and collapses together with a shell of the respective container, the respective wall folds of the shell and insert meshing together to result in a combined collapsed vertical dimension as small or nearly as small as that of the collapsed shell alone.