Data has become an important factor of production alongside land,labor,capital,technology,etc.By leveraging data analysis to mine potential value,we can uncover profound insights into consumer behavior,market trends,and production efficiency,thereby promoting industrial innovation,technology upgrades,and regional economic development.However,it may cause privacy leakage problems when we use and share data.This oversight has also led to more serious issues,such as the leakage of sensitive data and illegal cross-border data transfers.For instance,some financial companies,due to the absence of comprehensive privacy protection mechanisms in the processes of collecting,circulating,and utilizing user data,have experienced incidents where data is used and traded without user consent.As a result,it severely stops the data circulation and sharing.To further protect user data privacy,federated unlearning can rollback the data-generated training updates to the machine learning model,which can further protect the data privacy and security of users.In this paper,we review the research work of federated unlearning.Firstly,we conduct an in-depth analysis of the federated learning training architecture,highlighting the specific types of privacy leakage threats.To reduce the risk of privacy leaks,we introduce the concept and definition of unlearning,and list different unlearning scenarios,thereby seamlessly transitioning to the concept of federated unlearning.On this basis,we outline the processes involved in federated unlearning and introduce unlearning granularity and challenges.Secondly,the federated unlearning algorithms are divided into two categories,including global model-oriented and local model-oriented algorithms according to the modified object.We further subdivide into several subcategories based on two major categories and analyze the implementation details of each algorithm in depth.To further compare the strengths and weaknesses,we conduct detailed comparative analyses across different categories of algorithms,focusing on aspects such as algorithm performance,types of requesters,and forgetting requests.Additionally,we also conducted an experiment to show the performance of different categories of federated unlearning algorithms in terms of model accuracy.Thirdly,the commonly used performance metrics are divided into three categories,including model performance metrics,forgetting effect metrics,and privacy protection metrics.We conduct a detailed comparison and analysis of these metrics in terms of the unlearning stage,as well as their advantages and drawbacks.Fourthly,we summarize the research and applications of federated unlearning in privacy protection and attack resistance,including the protection of commercial information privacy,federated recommendation systems and federated clustering,etc.Finally,this paper looks forward to the future research directions of unlearning algorithms and applications from the personalized perspective,including promoting the market circulation of data elements,deletion of low-quality data,forgetting applications in cross-domain machine learning,customized services,and federated unlearning in special scenarios.