Artificial intelligence (AI), including deep and traditional machine learning, holds great promise for advancing biomedical research and healthcare. However, most AI studies remain academic in nature and rarely transition into clinical practice, largely due to limited access to diverse real-world datasets. Centralized learning, the traditional approach to multi-institutional collaboration, is hindered by privacy, legal, and logistical barriers. Federated learning (FL) offers a decentralized alternative, enabling institutions to collaboratively train models without sharing sensitive patient data. This article reviews key algorithmic, privacy, and practical developments in FL for biomedical engineering, including strategies to handle non-identical data distributions and safeguard privacy through differential privacy, secure aggregation, and confidential computing. We also discuss current limitations and considerations for the need of scalable, interoperable infrastructures. FL represents a paradigm shift toward building generalizable, equitable, and clinically impactful AI models. Realizing this vision requires continued advances, such as FL-as-a-service platforms and regulatory-aligned workflows that support persistent and trustworthy model deployment to truly realize AI's promise in patient care.