In recent years, the network dependency and interdependent networks have become a research hotspot in the field of complex network, but literature about the overview of related research progress is still very rare. Based on the systematic research of domestic and overseas literatures, the percolation theory of the interdependent networks was briefly introduced, and the cascading failure process of the interdependent networks was described. Then the related progress was summarized from three aspects that can affect the robustness of interdependent networks: characteristics of sub network, type of dependency edge, the combination of sub networks. Finally, the future development direction of interdependent networks was prospected in both theoretical and practical aspects.