The current status of research in the design of heterogeneous catalysts based on metal-organic frameworks (MOFs) and their application in various processes is discussed. Particular attention is given to reactions pertaining to selective catalysis. It has been shown that metal-organic frameworks successfully compete with the classical molecular sieves zeolites in this area. However, MOFs are still not able to replace these inorganic systems in the cases when a catalytic reaction requires severe conditions. Their primary fields of application are fine organic synthesis and enantioselective catalysis, since the relevant catalytic processes can be carried out under mild conditions.