The current literature compares the dark matter model and the modified Newtonian dynamics theory, and respectively explains how they solve the existing problems of astronomical observations. Furthermore, we introduce the development of dark matter model, list the main important evidence and prospective candidates for dark matter, and summarize the existing methods to detect dark matter and their limitations. In addition, this literature introduces the development of the modified Newtonian dynamics theory, and summarizes the problems to be solved and the significant current progress. Finally, we compare the advantages and limitations of these two theories, and discuss the significance of this research and the future research direction.