The most important and interesting results obtained at the Topchiev Institute of Petrochemical Synthesis of the Russian Academy of Sciences in 2008-2015 concerning dimethyl ether conversion to lower olefins in the presence of HZSM-5 zeolite catalysts have been systematized and summarized. The effects of the nature of the modifying element and catalyst steaming on the structural, acidic, and catalytic properties of the zeolite catalyst have been discussed. Some features of the influence of steam present in the feed gas mixture as a function of the nature of the modifying element have been elucidated. Data on the effect of impurities in the feed mixture (methanol and steam) have been described.