The visual systems of insects are exquisitely sensitive to motion. Over the past 40 years or so, motion processing in insects has been studied and characterised primarily through the optomotor response. This response, which is a turning response evoked by the apparent movement of the visual environment, serves to stabilise the insect's orientation with respect to the environment. Research over the past decade, however, is beginning to reveal the existence of a variety of other behavioural responses in insects, that use motion information in different ways. Here we review some of the recently characterised behaviours, describe the inferred properties of the underlying movement-detecting processes, and propose modified or new models to account for them.