Biosensors integrated with artificial intelligence (AI) hold immense potential for transforming healthcare through rapid, automated diagnostics and precision therapeutics. This paper reviews the convergence of biosensing and AI towards developing smart biomedical systems. The fundamentals, historical evolution, and classification of biosensors are presented, highlighting key applications across infections, chronic illnesses, and environmental monitoring. Core AI concepts, including machine learning, neural networks, computer vision, and natural language processing, are discussed, along with their implementation to augment biosensor functionality, connectivity, point-of-care adoption, and laboratory automation. Promising research directions and real-world case studies applying AI-integrated biosensors for early diagnosis and drug delivery are discussed. The opportunities and challenges in advancing this synergistic technology are contemplated, underscoring the need for cross-disciplinary collaboration, clinical validation, ethical vigilance and supportive policy environments to successfully translate AI-biosensors into practical healthcare solutions.