A remote controller and an image display apparatus controllable by the remote controller are disclosed. The image display apparatus includes a display, an interface for receiving from the remote controller a signal based on a motion of the remote controller or a signal based on a touch input on the remote controller, and a controller for operating the image display apparatus in motion mode to control the image display apparatus according to the motion of the remote controller, if the degree of the motion is equal to or larger than a reference value and operating the image display apparatus in touch mode to control the image display apparatus according to the touch input on the remote controller, if the degree of the motion is smaller than the reference value.