Heterogeneous catalytic reactions of dimethyl ether (DME) with various compounds (alkenes, aromatic compounds, CO, etc.) are surveyed. Analysis of published data allows the conclusion that the formation of products generally involves surface intermediates produced by the interaction of DME with Bronsted acid sites. There is no formation of water in this case, suggesting that DME can be preferred to methanol in some cases. Surface intermediates CH*(3) which are bound to the oxygen atoms of the zeolite lattice (methoxides) and retain their reactivity in the case of temperature elevation to 473 K have been identified using IR, UV, and in situ high-resolution solid-state NMR spectroscopy. Based upon the data on the state of intermediates that are formed from DME on the surface of heterogeneous catalysts, a series of catalytic reactions involving DME, namely, methylation of alkenes and aromatic compounds, carbonylation, synthesis of ethanol, and partial oxidation resulting in a set of compounds have been considered. Some reactions, such as carbonylation of DME by synthesis gas, synthesis of ethanol, and synthesis of dimethoxymethane and polyoxymethylene dimethyl ether, are of industrial interest.