The anterior one-fifth of the human eye is called the cornea. It consists of several specialized cell types that work together to give the cornea its unique optical properties. As a result of its smooth surface and clarity, light entering the cornea focuses on the neural retina allowing images to come into focus in the optical centres of the brain. When the cornea is not smooth or clear, vision is impaired. The surface of the cornea consists of a stratified squamous epithelium that must be continuously renewed. The cells that make up this outer covering come from an adult stem cell population located at the corneal periphery at a site called the corneal limbus. While engaging in the search for surface markers for corneal epithelial stem cells, vision scientists have obtained a better understanding of the healthy ocular surface. In this review, we summarize the current state of knowledge of the ocular surface and its adult stem cells, and analyse data as they now exist regarding putative corneal epithelial stem cell markers.