This review discusses how drops can levitate on a cushion of vapor when brought in contact with a hot solid. This is the so-called Leidenfrost phenomenon, a dynamical and transient effect, as vapor is injected below the liquid and pressed by the drop weight. The absence of solid/liquid contact provides unique mobility for the levitating liquid, contrasting with the usual situations in which contact lines induce adhesion and enhanced friction: hence a frictionless motion, and the possibility of bouncing after impact. All these characteristics can be combined to create devices in which selfpropulsion is obtained, using asymmetric textures on the hot solid surface.