The shape descriptors based on spectral analysis have achieved good matching results in 3D non-rigid shape matching, which have attracted wide attention of researchers. Spectral analysis is an intrinsic shape analysis method based on spectral decomposition of Laplace-Beltrami operator on manifold, including spectral shape descriptors and spectral distance distribution functions, which have different mathematical properties and physical meanings. Based on two different types of shape descriptors, this paper gives a detailed method analysis and its application in shape matching. Firstly, this paper provides a 3D non-rigid shape matching framework by applying the shape descriptors based on spectral analysis, and the basic ideas and calculation methods of several commonly used spectral shape descriptors and spectral distance distribution functions are introduced. Secondly, this paper analyzes and compares the advantages and disadvantages of these methods and their application scenarios and provides reference for researchers to choose shape descriptors based on spectral analysis. Finally, the robustness, time consumption, and non-rigid matching performances of different shape descriptors based on spectral analysis are compared through experiments to promote the application process of shape descriptors based on spectral analysis.