Phase-only holograms are used widely in holographic three-dimensional display owing to their high diffraction efficiency and no conjugate image. An iterative algorithm plays an important role in generating phase-only holograms because of its flexible calculation and high-quality image reconstruction. This study introduced a comparative study on the latest iterative algorithms for generating phase-only holograms. The basic principle of generating phase-only holograms by iterative algorithm was introduced, and representative and innovative algorithms were realized by programming. Experiments were performed to analyze the characteristics, advantages, and disadvantages of various methods by comparing the image reconstruction quality and computation time. The results show that the histogram compensation algorithm can obtain better results for images with large pixel differences, the adaptive weighted Gerchberg-Saxton algorithm can be used for images with high reconstruction quality.