The complex biology of wound healing is an area in which theoretical modelling has already made a significant impact. In this review article, the authors describe the key features of wound healing biology, divided into four components: epidermal wound healing, remodelling of the dermal extracellular matrix, wound contraction, and angiogenesis. Within each of these categories, previous modelling work is described, and the authors identify what they regard as the main challenges for future theoretical work.