Materials design is an important component of modern science and technology, yet traditional approaches rely heavily on trial-and-error and can be inefficient. Computational techniques, enhanced by modern artificial intelligence (AI), have greatly accelerated the design of new materials. Among these approaches, inverse design has shown great promise in designing materials that meet specific property requirements. In this mini-review, we summarize key computational advancements for materials design over the past few decades. We follow the evolution of relevant materials design techniques, from high-throughput forward machine learning (ML) methods and evolutionary algorithms, to advanced AI strategies like reinforcement learning (RL) and deep generative models. We highlight the paradigm shift from conventional screening approaches to inverse generation driven by deep generative models. Finally, we discuss current challenges and future perspectives of materials inverse design. This review may serve as a brief guide to the approaches, progress, and outlook of designing future functional materials with technological relevance.