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With annually increased coal mining depth, gas extraction becomes more and more problematic. The gas extraction effect depends on coal seam permeability, which, in turn, is affected by many factors, including loading and unloading stresses and strains in the coal seam. Stresses induce internal cracks, resulting in cleats and gas emission channels, the coal seam permeability permanently changes accordingly. To clarify the stress-induced effects on coal seam permeability, this survey summarized the available approaches used to link the stress path and seepage law in the coal body seepage law, which can be classified into two design methods: single load variation and combined field mining method. The characterization methods used to observe the surface of coal samples and three-dimensional reconstruction include electron microscopy, CT scanning, and Nuclear Magnetic Resonance (NMR). According to the stress paths designed by the above two approaches, the seepage laws and similarities of three kinds of coal samples with the fractured structure were summarized in this paper. The following directions are recommended to study the seepage law of coal bodies with three kinds of fractured structures under stress. Firstly, the stress path of the experimental coal body should be designed by the combined field mining method. The stressed environment of a deep coal seam is complicated, and the axial and confining pressures change simultaneously. Therefore, one cannot fully reflect the real situation on-site by studying permeability evolution alone. Secondly, during the coal seam mining, the stressed state changes from time to time, and the development of coal seam fractures is affected by mining. When studying the stress effect on seepage of coal samples, the fractured structure of coal samples should be considered. Finally, the available structural characterization methods of coal samples can be combined with the 3D printing technology, which would produce artificial samples with the fractured structure characteristics of natural coal.