The AI-driven inverse design paradigm is fundamentally transforming materials discovery research by enabling the computational exploration of novel materials with predefined target properties. This review comprehensively synthesizes recent progress in applying AI methodologies, such as generative models, reinforcement learning, and diffusion models, to diverse material classes including metals, polymers, and proteins. It particularly highlights key advancements, such as the AI-guided discovery of high-entropy alloys with superior mechanical properties and the de novo design of functional polymers and protein-based biomaterials. Furthermore, major remaining challenges are discussed, including the computational-to-experimental validation gap, data scarcity, and the need for physically constrained models. Furthermore, this review explores the emerging frontier of Quantum Machine Learning (QML), which holds the promise of overcoming the limitations of classical computing for particularly complex problems in materials simulation. Finally, the integration of these methodologies into fully autonomous laboratories for closed-loop design, synthesis, and characterization is presented as a transformative route to accelerate the materials discovery cycle.