For organisms that fly or swim, movement results from the combined effects of the moving medium - air or water - and the organism's own locomotion. For larger organisms, propulsion contributes significantly to progress but the flow usually still provides significant opposition or assistance, or produces lateral displacement ('drift'). Animals show a range of responses to flows, depending on the direction of the flow relative to their preferred direction, the speed of the flow relative to their own self-propelled speed, the incidence of flows in different directions and the proportion of the journey remaining. We here present a classification of responses based on the direction of the resulting movement relative to flow and preferred direction, which is applicable to a range of taxa and environments. The responses adopted in particular circumstances are related to the organisms' locomotory and sensory capacities and the environmental cues available. Advances in biologging technologies and particle tracking models are now providing a wealth of data, which often demonstrate a striking level of convergence in the strategies that very different animals living in very different environments employ when moving in a flow.