In the field of holographic three-dimensional (3D) display, the development of fast algorithms with which to generate computed holograms is an important research task, as the generation of computed holograms is currently time-consuming. The wavefront recording plane (WRP) technique is an effective method to accelerate the generation of holograms based on point clouds. This study analyzes the latest progress in the development and application of the WRP technique for computed holograms. We first introduce the principles of the WRP technique, before going on to analyze the latest research methods for wavefront recording in detail. We summarize and analyze the ways in which these techniques are used to accelerate the generation of the computed hologram and to improve the quality of 3D image reconstruction, and we also review special applications such as surface holographic imaging. We analyze the current utility of the various WRP methods for increasing the speed of computation, improving the quality of image reconstruction, reducing the size of the look-up table in computer memory, increasing the field-of-view angle, and removing aliasing noise. The role of the WRP technique in the creation of real-time, dynamic, high-quality, and large-view holographic 3D displays is also analyzed. Finally, the advantages and disadvantages of various methods are analyzed, and future directions for the development of the WRP technique are proposed.