In real life, most of the infrastructure networks closely related to the national economy and people's livelihood do not exist independently, but are interconnected with or dependent on each other, so the multilayer network model is proposed to study the independent complex systems and infrastructures. When the nodes in the multilayer network suffer initial failure or attack, the cascade occurs due to the interaction between the “intra-layer” and “inter-layer”, and the failure can propagate in the network layer and across the layers iteratively, so that the scale of the failures is enlarged gradually. As a result, many multilayer networks are more fragile than single networks. The cascading failure of multilayer network usually brings very serious catastrophes to our society. So, conducting the research on preventing the multilayer network from cascading failure and recovering is of great significance. As far as the prevention of cascading failure is concerned, what are mainly included are the strategies such as the fault detection, the protection of important nodes, the optimization of the coupling method of networks, and the backup of nodes. As for the recovery of multi-layer network, included mainly are the strategies such as common boundary node recovery, the idle connected link recovery, the link addition, the priority recovery of important nodes, the topology perturbation, and the repairing of localized attack and adaptive link.