Corneal epithelium has a highly specialided wound-healing response. The biological aspects of this repair process are reviewed, and methods of modelling it mathematically are described. A model which focuses on the source of epidermal growth factor (EGF) within a healing wound id described. By considering mathematical representations of a number of possible source terms, it is shown that the EGF presents in the tear film is insufficient to explain the observed rate of healing, and experimental approaches are suggested for distinguishing between other sources. Also, the simulation of exogenous addition of EGF using the miodel is described. An issue that has been the subject of considerable debate in the literature is the role of eyeball curvature. The model is used to show that this curvature is not significant for either the speed or form of healing in the epithelium. In conclusion, a comparison is made between wound healing in the corneal epithelium with that in the epidermis of the skin. Possible diredtions for future modelling work are considered.