The main events in the development of membrane catalysis are presented in this paper. The pioneering studies of Graham performed in London were continued by Zelinskii in Moscow and by Snelling in the USA. The finding by Frost in the USSR that hydrogen evolved from Pd film is much more active in hydrogentation than feeded as gas with the hydrogenable substance stimulated the researchers of several countries, including the author of this paper, who proposed the method for carrying out simultaneously dehydrogenation on one surface of membrane catalyst and hydrogenation by the diffused hydrogen on the other surface. Similar reactions couplings were carried out later but independently performed by Pfefferle in the USA. The types of hydrogen porous membrane catalysts for selective hydrogenation and dehydrogenation elaborated in Russia were described in next sections. The final section deals with the examples of coupling of hydrogen evolution and consumption reactions on membrane catalyst as well as on the systems of membrane and granular catalysts.