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At present, the controllability of complex networks is a hot issue in complex networks domain. From the perspective of graph theory, in the paper quite a few pioneering works on the controllability of complex networks were introduced, and the latest progress of the controllability of complex networks was emphatically summarized. In addition, the paper mainly discussed the basic ideas and effective methods to enhance the structural controllability of complex networks and analyzed the advantages and disadvantages of different methods. Finally, several problems and possible development directions of the controllability of complex networks were summarized.