The integration of artificial intelligence into hearing assistance marks a paradigm shift from traditional amplification-based systems to intelligent, context-aware audio processing. This systematic literature review evaluates advances in AI-driven selective noise cancellation (SNC) for hearing aids, highlighting technological evolution, implementation challenges, and future research directions. We synthesize findings across deep learning architectures, hardware deployment strategies, clinical validation studies, and user-centric design. The review traces progress from early machine learning models to state-of-the-art deep networks, including Convolutional Recurrent Networks for real-time inference and Transformer-based architectures for high-accuracy separation. Key findings include significant gains over traditional methods, with recent models achieving up to 18.3 dB SI-SDR improvement on noisy-reverberant benchmarks, alongside sub-10 ms real-time implementations and promising clinical outcomes. Yet, challenges remain in bridging lab-grade models with real-world deployment - particularly around power constraints, environmental variability, and personalization. Identified research gaps include hardware-software co-design, standardized evaluation protocols, and regulatory considerations for AI-enhanced hearing devices. Future work must prioritize lightweight models, continual learning, contextual-based classification and clinical translation to realize transformative hearing solutions for millions globally.