Hydrogen is a significant industrial raw material and clean fuel, and hydrogen separation has significant social and economic values. Membrane separation has a wide application prospect in hydrogen separation as it uses simple devices, is environmentally friendly, and has high conversion efficiency and low cost of investment. Hydrogen separation membranes remain a research focus as their performance is the major factor that determines hydrogen separation efficiency. This study summarized the application demand and basic mechanism of hydrogen separation membranes and reviewed the research progress of dense metal, porous inorganic, metal-organic framework (MOF), organic polymer, and hybrid matrix membranes. Specifically, although porous inorganic, organic polymer, and hybrid matrix membranes have good hydrogen separation and purification performances, their separation performance still requires improvement when they are applied in distributed and small application scenarios. Improving the anti-poisoning performance of palladium-based metal membranes and optimizing the cost-effectiveness are effective ways to promote industrial application of membranes. Combining the advantages of porous inorganic and MOF membranes can facilitate the significant development of molecular sieving membranes. The high-temperature resistance and mechanical properties of organic polymer membranes require improvement. Modifying existing polymer membrane materials and preparing polymer alloys are two major directions for developing novel gas separation membranes. The performance of hybrid matrix membrane can be notably improved after controllable adjustment of its distribution. The research and application of multiple membranes has supported hydrogen separation and purification, and these membrane techniques will continue creating more engineering values once the number of available materials is increased and the preparation technologies are advanced in the future.