Renewal of stratified squamous epithelia, eg, the epidermis, the esophagus, or the epithelia lining the oral cavity, normally depends on the presence of keratinocyte stem cells that are thoroughly distributed in the epithelial basal layer. It is commonly thought that stem cells divide asymmetrically and generate transient amplifying cells. In turn, the latter generate postmitotic cells, which will replace the terminally differentiated cells that constantly slough off the epithelial surface. In this model, each stem cell only renews a tiny epithelial column, even if it has the capacity to generate a large amount of epithelium, a property important during wound healing. Interestingly, the cornea is an exception among stratified epithelia, because it does not contain stem cells but rather relies on the centripetal migration of transient amplifying cells generated by stem cells dividing occasionally and located at the limbus, the transition zone of the cornea with the conjunctiva. It is unclear which evolutionary advantage an epithelium with a rapid turn over has gained through the development of such a mechanism. Understanding why and how the cornea has evolved differently from all other stratified epithelia is certainly a major challenge in epithelial stem cell biology.