Abstract: Collective cell migration is a commonly recurring theme in biology and medicine, with examples in developmental biology, wound healing, and disease. For example, in solid tumours, new blood vessels are created by the process of angiogenesis and these then supply the tumour with nutrients and also a way to metastasize. In developmental biology, neural crest cells migrate long distances to form structures, such as the lining of the gut, cranial features etc. I will survey a number of mathematical models that have been proposed for these phenomena and describe how they have been used to generate new biological insights.