The cornea is subject to a myriad of ocular conditions often attributed to cell loss or cell dysfunction. Owing to the superficial positioning of tissues composing the anterior segment of the eye, particularly the cornea, regenerative medicine in this region is aided by accessibility as compared with the invasive delivery methods required to reach deep ocular tissues. As such, cell therapies employing the use of carrier substrates have been widely explored. This review covers recent advances made in the delivery of stem cells, corneal epithelial cells, and corneal endothelial cells. Particular focus is placed on the most popular forms of synthetic scaffolds currently being examined: contact lenses, electrospun substrates, polymeric films, and hydrogels.