Generative models have emerged as transformative tools in materials science, enabling the inverse design of novel materials with tailored properties by learning from vast datasets of structures and compositions. This review synthesizes recent advancements in generative approaches, including variational autoencoders, generative adversarial networks, diffusion models, and large language models. It highlights their conceptual capabilities for accelerating discovery while addressing scientific limits such as data scarcity, synthesizability, and interpretability. By examining applications in inorganic crystals, organic molecules, and energy materials, we delineate how these models bridge computational efficiency with experimental validation, yet face challenges in generalizability and physical fidelity. Future directions emphasize hybrid physics-informed architectures and closed-loop automation to overcome current barriers and unlock sustainable materials innovation.