Molybdenum disulfide is a layered transition metal chalcogenide semiconductor. It has many applications in the fields of two-dimensional spintronics, valleytronics and optoelectronics. In this review, molybdenum disulfide is taken as a representative to systematically introduce the energy band structures of single layer, bilayer and twisted bilayer molybdenum disulfide, as well as the latest experimental progress of its realization and low-temperature electrical transport, such as superconductivity and strong correlation phenomenon. Finally, two-dimensional transition metal chalcogenide moiré superlattice’s challenges in optimizing contact and sample quality are analyzed and the future development of this field is also presented.