This paper summarizes the key points and state-of-the-art of researches on cascading failures，including the evolution mechanism，mode expression and scene screening criteria.It is suggested that the termliansuo faults”with Chinese pinyin might be used only if the causality between two successive faults needs stress.Otherwise，the termxiangji faults”with Chinese pinyin is more suitable for covering successive faults with independent causes or common causes.The methods for identifying key successive-fault-chains can be classified by the applied attention indices，such as the probability-based，the consequence-based and the risk-based ones.These methods and their effects are compared.This paper also points out new challenges and possible breakthroughs on the relevant researches and applications，especially for correct handling of small- probability and high-risk faults.