This paper systematically reviews the development of AI-based hearing assistance technology, especially AI-based selective noise cancellation (SNC) technology. AI-based SNC technology represents a paradigm shift from conventional amplified hearing assistance systems to intelligent and context-aware audio processing. This paper synthesizes and analyzes research results from various aspects, including deep learning architecture, hardware implementation strategy, clinical validation studies, and user-centered design. It traces the development from early machine learning models to the latest convolutional recurrent networks (CRNNs) and transformer-based architectures, and presents significant performance improvements (up to 18.3 dB SI-SDR improvement) over existing methods, real-time implementations in less than 10 ms, and promising clinical outcomes. However, it points out challenges such as power constraints, environmental changes, and personalization for deployment in real environments, as well as research gaps such as hardware-software co-design, standardized evaluation protocols, and regulatory considerations for AI-enhanced hearing devices, and suggests future research directions for lightweight models, continuous learning, context-based classification, and clinical applications.