Collective motion is ubiquitous in biology, occurring in normal development, wound healing, and pathological cases, such as cancer. Here, I will review work that we have done on three problems: neural crest cell invasion, angiogenesis, and epithelial sheet movement. Each of these requires a different modelling paradigm, ranging from agent-based models, to partial differential equations. I will show how these problems lead to new mathematical challenges and how, with close collaboration with experimentalists, in some cases we have unearthed new biology.