As an important topological material, α-Sn (also known as grey tin) can be turned into many topological phases including topological insulator and topological semimetal by breaking its symmetry. Until now, the study on α-Sn has been mainly focused on the topological band structures by theorical calculation and angle resolved photoemission spectroscopy (ARPES), while the epitaxial growth of α-Sn and its electronic transport properties are seldom reported due to the substrate contribution. In this paper, the research progress of α-Sn is reviewed based on the recent progress made by our group, including the epitaxial growth of high quality α-Sn films by molecular beam epitaxy (MBE), the methodology of transport measurements and topological property investigation. The transport evidence of topological semimetal phase and spin-polarized topological surface state in α-Sn is demonstrated and the topological property is engineered by thickness and strain, etc. This work provides not only important evidences for further investigation on the topological property of α-Sn, but also an essential material platform for novel quantum devices based on α-Sn.