Assemblies for storing, handling, transporting, viewing, evaluating, and/or shipping corneal tissue are provided. The completed fitted assembly supports and allows for transporting a graft or implant with an assembly that comprises; a vial that is either cylindrical or rectangular cuboid and lid that includes a poly-cone insert, a support base so that the vial is able to stand upright and remain motionless, support columns integrated seamlessly within the vial with apertures that provide for full fluid communication and notches for positioning and support of an assembled corneal tissue carrier that is suited to accommodate compressive force generated between said lid and said notches, in addition to being able to accommodate a tissue carrier assembly via compression forces between said lid and a bottom surface of said vial, and a rectangular cuboid shape that also includes a flat transparent surface that provides inspection of corneal tissue visually or via instrumentation.