Plants have evolved a multitude of mechanisms to actuate organ movement. The osmotic influx and efflux of water in living cells can cause a rapid movement of organs in a predetermined direction. Even dead tissue can be actuated by a swelling or drying of the plant cell walls. The deformation of the organ is controlled at different levels of tissue hierarchy by geometrical constraints at the micrometre level (e.g. cell shape and size) and cell wall polymer composition at the nanoscale (e.g. cellulose fibril orientation). This paper reviews different mechanisms of organ movement in plants and highlights recent research in the field. Particular attention is paid to systems that are activated without any metabolism. The design principles of such systems may be particularly useful for a biomimetic translation into active technical composites and moving devices.