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In this article, we conducted a thorough review of the related works, following the development context and deeply mining the key technologies behind FL from the perspectives of theory and application. Specifically, we first classify the existing works in FL architecture based on the network topology of FL systems with detailed analysis and summarization. Next, we abstract the current application problems, summarize the general techniques, and frame the application problems into the general paradigm of FL base models. Moreover, we provide our proposed solutions for model training via FL. We have summarized and analyzed the existing FedOpt algorithms, and deeply revealed the algorithmic development principles of many first-order algorithms in depth, proposing a more generalized algorithm design framework. With the instantiation of these frameworks, FedOpt algorithms can be simply developed. As privacy and security are the fundamental requirements in FL, we provide the existing attack scenarios and the defense methods. To the best of our knowledge, we are among the first tier to review the theoretical methodology and propose our strategies since there are very few works surveying the theoretical approaches. Our survey targets motivating the development of high-performance, privacy-preserving, and secure methods to integrate FL into real-world applications.<\/jats:p>","DOI":"10.1145\/3664650","type":"journal-article","created":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T09:07:44Z","timestamp":1717232864000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["Advancements in Federated Learning: Models, Methods, and Privacy"],"prefix":"10.1145","volume":"57","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4179-3815","authenticated-orcid":false,"given":"Huiming","family":"Chen","sequence":"first","affiliation":[{"name":"Tsinghua University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6382-0861","authenticated-orcid":false,"given":"Huandong","family":"Wang","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0179-0991","authenticated-orcid":false,"given":"Qingyue","family":"Long","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0419-5514","authenticated-orcid":false,"given":"Depeng","family":"Jin","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5617-1659","authenticated-orcid":false,"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing China"}]}],"member":"320","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"2021. 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