Hydrogen, one of the most promising energy carriers for the future, is currently produced mainly by natural gas reforming or coal gasification, where mixtures containing H₂, CO₂ and contaminants like CO, H₂S and CH₄ are obtained. Among other methods, membrane technology has received special attention due to its potential efficiency for hydrogen separation, simplicity of operation, low energy consumption, and because it is environmentally friendly. For this application, the inorganic membranes can be essentially divided into five main families: metallic and proton conducting (dense phases), and silica, zeolite and carbon molecular sieve (porous solids). Over the past 20 years, palladium-based membranes have been the most studied and implemented at industrial level; however, recent advances in other membrane types have received a great deal of attention. This article critically reviews more than 520 publications, highlighting the latest research developments on inorganic membranes for the recovery and purification of hydrogen, with emphasis on their structural characteristics, synthesis, commercial application, drawbacks and challenges. Furthermore, a large compilation of data is provided in Supplementary Material divided according to membrane type.