Abstract: Federated learning is designed for data privacy and data security issues, after a large number of clients are trained locally in a distributed manner, the central server then aggregates the model parameter updates provided by each local client, but the central server is unable to see how these parameters are updated, and this feature creates a serious security issue, i.e., a malicious participant can train a poisoned model and upload the parameters in the local model, and then globally model to introduce backdoor features. In this paper, we focus on the security and robustness research under the scenarios specific to federated learning, i.e., backdoor attack and defense, summarize the scenarios that generate backdoor attacks under federated learning, summarize the latest methods of backdoor attack and defense under federated learning, and compare and analyze the performance of the various attack and defense methods, revealing their advantages and limitations. Finally, we point out various potential directions and new challenges for backdoor attacks and defenses under federated learning.