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Zero resistance and Meissner effect are two crucial experimental evidences of superconductivity in determining a new kind of superconductor, which can be detected by transport and diamagnetic measurements. In this paper, we briefly review the main transport and magnetization results on the one unit cell (1-UC) FeSe films grown on SrTiO3 (STO) substrates from our team in recent years, which identify the high temperature superconductivity in 1-UC FeSe films.