Currently, the treatment of corneal diseases caused by damage to the corneal endothelium requires a donor cornea. Because of their limited availability (1 donor cornea for 70 patients in need), researchers are investigating alternative approaches that are independent of donor tissue. One of them includes the development of a tissue engineered scaffold onto which corneal endothelial cells are seeded. In order to function as a suitable substrate, some of its essential properties including thickness, permeability, transparency and mechanical strength should meet certain demands. Additionally, the membrane should be biocompatible and allow the formation of a functional endothelium on the surface. Many materials have already been investigated in this regard including natural, semi-synthetic and synthetic polymers. In the current review, we present an overview of their characteristics and provide a critical view on the methods exploited for material characterization. Next, also the suitability of scaffolds to serve their purpose is discussed along with an overview of natural tissues (e.g. amniotic membrane and lens capsule) previously investigated for this application. Eventually, we propose a consistent approach to be exploited ideally for membrane characterization in future research. This will allow a scientifically sound comparison of materials and membranes investigated by different research groups, hence benefitting research towards the creation of a suitable/optimal tissue engineered endothelial graft.