The rapid generation technology of computer-generated hologram (CGH) is the key technology of the holographic three-dimensional display system. The calculation of holograms based on point source model is an important branch of computational holography because of its simple model and flexible operation. However, the calculations of point source model for holograms are enormous. In order to meet the requirements of real-time display, the methods of improving the calculation speed of hologram have been put forward continuously. The development of the fast algorithm of point source model is reviewed. Based on the principle of CGH, according to the research direction of the fast algorithm of point source model, it is divided into two categories: algorithm, and combination of algorithm and high-performance hardware. Through the analysis of the implementation methods and existing problems of all kinds of algorithms, the direction of improvement is pointed out, and the contribution of high-performance hardware to CGH is introduced. Finally, the future research direction of point source model fast algorithm is prospected.