A 'nowcast' is a type of weather forecast which makes predictions in the very short term, typically less than two hours - a period in which traditional numerical weather prediction can be limited. This type of weather prediction has important applications for commercial aviation; public and outdoor events; and the construction industry, power utilities, and ground transportation services that conduct much of their work outdoors. Importantly, one of the key needs for nowcasting systems is in the provision of accurate warnings of adverse weather events, such as heavy rain and flooding, for the protection of life and property in such situations. Typical nowcasting approaches are based on simple extrapolation models applied to observations, primarily rainfall radar. In this paper we review existing techniques to radar-based nowcasting from environmental sciences, as well as the statistical approaches that are applicable from the field of machine learning. Nowcasting continues to be an important component of operational systems and we believe new advances are possible with new partnerships between the environmental science and machine learning communities.