Federated learning represents a paradigm shift in how machine learning models are trained, moving from centralized data collection to distributed computation across edge devices. This article provides an in-depth look at federated learning approaches and applications.\n\nWe explain the core principles of federated learning, including local model training, secure aggregation, and differential privacy integration. The article covers applications in mobile keyboards, healthcare consortia, and Internet of Things networks.\n\nWe also discuss technical challenges such as communication efficiency, model personalization, and defense against adversarial attacks in federated settings.