Federated learning (FL) is a promising technique for resolving the rising privacy and security concerns. Its main ingredient is to cooperatively learn the model among the distributed clients without uploading any sensitive data. In this paper, 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 is the fundamental requirement 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.

联邦学习（FL）是解决日益严重的隐私和安全问题的一种很有前景的技术。其主要内容是在分布式客户端之间协作学习模型，而无需上传任何敏感数据。本文对相关工作进行了全面回顾，顺应发展脉络，从理论和应用的角度深入挖掘FL背后的关键技术。具体来说，我们首先根据FL系统的网络拓扑对现有的FL架构工作进行分类，并进行详细的分析和总结。接下来，我们对当前的应用问题进行抽象，总结通用技术，并将应用问题框架到 FL 基础模型的通用范式中。此外，我们还提供了通过 FL 进行模型训练的建议解决方案。我们对现有的FedOpt算法进行了总结和分析，深入揭示了许多一阶算法的算法发展原理，提出了更通用的算法设计框架。通过这些框架的实例化，可以简单地开发FedOpt算法。由于隐私和安全是FL的基本要求，我们提供了现有的攻击场景和防御方法。据我们所知，我们是第一批回顾理论方法并提出我们的策略的人之一，因为调查理论方法的著作很少。我们的调查目标是激励开发高性能、隐私保护和安全的方法，将 FL 集成到现实世界的应用程序中。