An electronic device may have a hollow display cover structure. The hollow display cover structure may be formed from a structure having an inner surface. The structure may be an elongated member having a longitudinal axis. A material such as sapphire, other crystalline materials, or other transparent materials may be used in forming the hollow display cover structure. A flexible display layer such as an organic light-emitting diode display layer or other flexible display structure may be wrapped around the longitudinal axis to cover the interior surface of the hollow display cover structure. The electronic device may have a touch sensor, accelerometer, gyroscope, and other sensors for gathering input such as user input. The electronic device may use one or more sensors to gather information on rotational motion of the device and can display content on the flexible display layer accordingly.