A mode-switchable backlight and mode-switchable display employ a first planar backlight to emit broad-angle emitted light during a first mode and a second planar backlight to emit directional emitted light during a second mode. The second planar backlight includes a plate light guide and an array of multibeam elements configured to scatter out guided light from the light guide during a second mode as the directional emitted light including a plurality of directional light beams having principal angular directions corresponding to view directions of a multiview image. The mode-switchable display further includes a light valve array configured to modulate the broad-angle emitted light to provide a two-dimensional image during the first mode and to modulate the directional emitted light to provide a multiview image during the second mode.