Complexity science is one of the important frontier fields of science in the world now. In order to promote the application of the theories and methods of complexity science in the field of shale oil and gas research and exploration, focusing on the connotation of the complexity of geosystems. Methods: Based on a literature review, this paper introduces the basic theories and research methods of the complexity of geosystems from the aspects of multiple coupling and interaction of multiple components of geological system, space-time structure of geological process, self-organized critical dynamics of geological processes and the formation of mineral resources on the edge of chaos. Results: Applying the above complexity theory of geological system to shale oil and gas system, this paper discusses how to use the overall characteristics of complex system and the "emergence" mechanism of local component unit interaction to solve the problem of how to objectively describe the macroscopic reservoir characteristics by using microscopic local fine characterization in shale reservoir; analyses the method for establishing static and fractal space-time structure of shale reservoir heterogeneity with use of the space-time structure theory of geological process; explores the prediction method of shale oil and gas enrichment at the edge of chaos in self-organized critical state under the guidance of holism, according to the fractal growth law of geological system at the edge of chaos. Conclusions: The theories and methods of complexity science will play a more and more important role in the exploration and research of shale oil and gas.