State-of-the-art technologies of fabrication of transition metal dichalcogenide monolayers like MeX2, where Me = Mo, W; X = S, Se, Te, and their based heterostructures are considered. Results of theoretical modeling are analyzed and possibilities of band gap engineering by means of strains, impurities, vacancies, various layer stacking and combination of different materials are presented. It is shown that vacancies and impurities in the positions of metal atoms may drastically change the band gap, even leading to an appearance of metallic properties, whereas a substitution of chalcogen atoms by isovalent atoms changes the properties not so dramatically. Possible applications of heterostuctures with tunable band gaps for creation of transistors, light-emitting diodes, photoelectrochemical cells or photovoltaic devices are proposed and their advantages in comparison with commonly used analogues are discussed.