Corneal stem/progenitor cells are typical adult stem/progenitor cells. The human cornea covers the front of the eyeball, which protects the eye from the outside environment while allowing vision. The location and function demand the cornea to maintain its transparency and to continuously renew its epithelial surface by replacing injured or aged cells through a rapid turnover process in which corneal stem/progenitor cells play an important role. Corneal stem/progenitor cells include mainly corneal epithelial stem cells, corneal endothelial cell progenitors and corneal stromal stem cells. Since the discovery of corneal epithelial stem cells (also known as limbal stem cells) in 1971, an increasing number of markers for corneal stem/progenitor cells have been proposed, but there is no consensus regarding the definitive markers for them. Therefore, the identification, isolation and cultivation of these cells remain challenging without a unified approach. In this review, we systematically introduce the profile of biological characterizations, such as anatomy, characteristics, isolation, cultivation and molecular markers, and clinical applications of the three categories of corneal stem/progenitor cells.