Federated Learning: A Comprehensive Review of Algorithms, Optimisation Frameworks, and Real-World Applications

Federated Learning (FL) has become an important method for collaborative machine learning while keeping data private and following rules. Unlike traditional centralized learning, FL lets multiple clients—like mobile phones, hospitals, banks, or IoT devices-train a shared model together without sharing their raw data. This helps handle data ownership, separate data storage, and privacy regulations. This review provides a comprehensive, structured, and citation-rich synthesis of the field aimed at researchers and graduate students. We trace the evolution of FL from early distributed optimisation and distributed SGD to modern privacy-preserving, communication-efficient, and personalised federated systems. The paper systematically covers core algorithms (FedAvg, FedProx, SCAFFOLD, adaptive optimisers, and personalisation methods), systems-level aspects (client scheduling, compression, stragglers, communication protocols), and privacy/security foundations (differential privacy, secure aggregation, adversarial robustness). We also survey evaluation practices, benchmarks, application case studies, and emerging domains such as federated reinforcement learning and FL for large language models. The review synthesises open problems related to heterogeneity, personalisation, scalability, privacy–utility trade-offs, and realistic benchmarking. We conclude by outlining concrete research directions and offering practical recommendations for deploying FL in real-world systems.