An electronic device may have a flexible display. The electronic device may have housing portions that are rotatably coupled to each other so that the flexible display may fold along one or more bend axes. A device may have rollers that store a flexible display and that help deploy the display from within a housing when additional display area is desired. A touch screen in a housing may be overlapped by a flexible display that has been scrolled outwardly from the housing. Wireless transmitter and receiver circuitry may be used to convey image data to display driver circuitry. The display driver circuitry may display images on a pixel array in a flexible display based on the image data. Magnets may be used to outwardly bias edge-mounted bistable support structures to help prevent a rolled flexible display from wrinkling.