Assemblies for storing, handling, transporting, viewing, evaluating, and/or shipping corneal tissue are provided. The assembly includes a corneal tissue carrier, optimized for DSAEK and UT-DSAEK corneal grafts, within a transport vial, the transport vial removably coupled to a stabilization base, wherein the ease of access to the graft carrier allows administering the corneal tissue sample to a patient in rapid succession so that more surgeries can be performed by a single surgeon in a single day.