The process by which a skin wound heals is complicated and requires the concerted action of a large number of cell types, chemicals and fibres. There have been many attempts to mathematically describe the wound healing process using a variety of different mathematical approaches. In this talk, I will review some of the earlier mathematical models developed for wound healing and the biological impact they have made. My own research into the mathematical modelling of wound healing is aimed at informing clinical treatment of non-healing wounds by devising governing equations which capture the essential behaviour of the complex system. In this talk I will discuss several of these mathematical models, the clinical insight gained by numerical and analytical investigation of them and the future challenges that I see in this research area.