Federated learning trains statistical models on remote devices or data centers while keeping data local, addressing challenges in privacy, large-scale learning, and distributed optimization. This article discusses the unique characteristics and challenges of federated learning, current approaches, and future research directions. Key challenges include expensive communication, systems heterogeneity, statistical heterogeneity, and privacy concerns. Communication efficiency is improved through local updating, compression, and decentralized training. Systems heterogeneity requires methods that tolerate varying device capabilities and dropped devices. Statistical heterogeneity necessitates models that handle non-identically distributed data, with approaches like multi-task learning and meta-learning being explored. Privacy concerns are addressed through differential privacy, homomorphic encryption, and secure function evaluation. Future directions include improving communication efficiency, handling heterogeneity, enhancing privacy, and addressing production challenges like concept drift and cold starts. Federated learning is a growing field with significant potential for privacy-sensitive applications, requiring interdisciplinary research to overcome existing challenges.Federated learning trains statistical models on remote devices or data centers while keeping data local, addressing challenges in privacy, large-scale learning, and distributed optimization. This article discusses the unique characteristics and challenges of federated learning, current approaches, and future research directions. Key challenges include expensive communication, systems heterogeneity, statistical heterogeneity, and privacy concerns. Communication efficiency is improved through local updating, compression, and decentralized training. Systems heterogeneity requires methods that tolerate varying device capabilities and dropped devices. Statistical heterogeneity necessitates models that handle non-identically distributed data, with approaches like multi-task learning and meta-learning being explored. Privacy concerns are addressed through differential privacy, homomorphic encryption, and secure function evaluation. Future directions include improving communication efficiency, handling heterogeneity, enhancing privacy, and addressing production challenges like concept drift and cold starts. Federated learning is a growing field with significant potential for privacy-sensitive applications, requiring interdisciplinary research to overcome existing challenges.