Holographic three-dimensional (3D) display is a true 3D display technique, which can provide realistic image of a real object or a scene because holography has the ability to reconstruct both the intensity and phase information, i.e., the wave front of the object or scene. Therefore, it could allow the observers to perceive the light as it is scattered by the real object itself without any special eyewear, which is quite different from other 3D display techniques, such as stereoscopic displays and volumetric 3D displays. In this paper, the achievements and developments of the latest new holographic 3D displays are presented. Holographic 3D displays can be divided into static holographic 3D displays and dynamic holographic 3D displays. Here, we briefly introduce the principle of holographic 3D display technique and static holographic 3D displays, and focus on dynamic holographic 3D displays. Large-size, high-resolution and color static holographic 3D displays have already been successfully fabricated and applied in some areas, such as holographic 3D maps and holographic 3D images. However, dynamic holographic 3D displays based on both optical materials and spatial light modulators (SLMs) are still under research, which is a challenge to their applications. Some holographic researchers study the holographic 3D displays based on the SLMs for large-size and large view angle display, but it is difficult to realize them because of limitations of SLMs and there still needs much effort to solve these problems in SLMs. Other holographic researchers work on dynamic holographic materials, such as inorganic crystals, photorefractive polymer, photochromic material etc. The response time and diffraction efficiency are key factors to these materials. Compared with other holographic media, liquid crystals with super-fast response time (about 1 ms) have been reported, which makes it possible to realize video refresh-rate holographic displays. The achievements of dynamic holography, which are helpful for holographic 3D video applications, are presented. Recently, real-time dynamic holographic display has been obtained in super-fast response liquid crystal films, which makes it possible that large-size, high-definition, color holographic 3D video displayers are developed by using these liquid crystal films in the future.