Although there have been a desire to implement ideal three-dimensional (3D) displays, it is still challenging to satisfy commercial demands in resolution, depth of field, form factor, eye-box, field of view, and frame rate. Here, we propose shape scanning displays that may have extremely large depth of field (10cm-infinity) without loss of frame rate or resolution, and enough eye-box (7.5mm) with moderate field of view (30°). Furthermore, our prototype provides quasi-continuous focus cues as well as motion parallax by reconstruction of 120 tomographic layers. Shape scanning displays consist of a tunable lens, a display panel, and a spatially adjustable backlight. The synchronization of the tunable lens and spatially adjustable backlight could provide additional dimension of depth information. In summary, we introduce a novel 3D display technology called shape scanning displays that present superior performance in resolution, depth of field, and focus cue reproduction. This approach has a lot of potential to be applied for various field in 3D displays including head-up displays, tabletop displays, as well as head-mounted displays. It could be efficient solution for vergence-accommodation conflict as providing accurate focus cues.