The integrity of the cornea, the most anterior part of the eye, is indispensable for vision. Forty-five million individuals worldwide are bilaterally blind and another 135 million have severely impaired vision in both eyes because of loss of corneal transparency; treatments range from local medications to corneal transplants, and more recently to stem cell therapy. The corneal epithelium is a squamous epithelium that is constantly renewing, with a vertical turnover of 7 to 14 days in many mammals. Identification of slow cycling cells (label-retaining cells) in the limbus of the mouse has led to the notion that the limbus is the niche for the stem cells responsible for the long-term renewal of the cornea; hence, the corneal epithelium is supposedly renewed by cells generated at and migrating from the limbus, in marked opposition to other squamous epithelia in which each resident stem cell has in charge a limited area of epithelium. Here we show that the corneal epithelium of the mouse can be serially transplanted, is self-maintained and contains oligopotent stem cells with the capacity to generate goblet cells if provided with a conjunctival environment. Furthermore, the entire ocular surface of the pig, including the cornea, contains oligopotent stem cells (holoclones) with the capacity to generate individual colonies of corneal and conjunctival cells. Therefore, the limbus is not the only niche for corneal stem cells and corneal renewal is not different from other squamous epithelia. We propose a model that unifies our observations with the literature and explains why the limbal region is enriched in stem cells.