Abstract: On complex networks, large-scale cascading failures that are triggered by some small disturbances can lead to disastrous consequences. In order to satisfy demand of the people on the security and reliability of complex networks re- lated to the national economy and people's livelihood, the study on cascading failures on complex networks becomes a hot branch of complex networks research in recent years. hhe theoretical modeling is the basic and key problem for a- nalysis, prevention and control of cascading failures. Main developments of cascading failures on complex networks were survcyed,mainly including several types of cascading failures models and the relevant research results. Both the existing problems at present and the development trend were pointed out

Key words: Complex networks,Cascading failures,Robustness,Scale free network