Abstract: The advancement of cutting-edge technology produces huge data sets. The current data boom not only poses a challenge to the traditional theory of statistical inference but also expands its scope. An important area of statistical inference research is difference analysis using various data types. The two-sample test is the primary tool for difference analysis, which has always been the focus and hot spot in the statistical community. However, previous research on the two-sample test has been focused on Euclidean data, whereas related studies on non-Euclidean data are still in their infancy. This study reviews some common characteristics of existing nonparametric two-sample tests. Then, based on this information, we create new two-sample nonparametric tests for data with more complex structures. In addition, the problems facing this field of study are discussed.