Von Neumann Architecture is the foundation of modern computer. In the first half of this paper, several characteristics of von Neumann architecture are discussed in detail. Due to the tradition of von Neumann computer architecture. Natural limitations limit the development of computers. In recent years, people strive to break through the limitations of the traditional von Neumann system, and the research on various non- Neumann computers is booming. In the second half of this paper, four typical non-von Neumann architectures are introduced, which are Harvard architecture, photon computer, quantum computer and neural computer. This paper discusses the four research directions that may break through the von Neumann architecture at present, and analyzes some characteristics of the four different research directions. At last, the overall content of the article is summarized profoundly, which affirms the important role of von Neumann architecture, and believes that the research of non-von Neumann architecture has made great progress. Looking forward to the advent of non-von Neumann computers in the future.