On Apr. 7, 2021, the Muon g-2 collaboration at Fermilab announced the latest experimental result of the anomalous magnetic moment. After combining with the previous result at the Brookhaven National Laboratory, the new average of the experimental value is differing from the Standard Model prediction by 4.2 standard deviations, a strong hint of physics beyond the Standard Model. In this article, a history of the magnetic moment of elementary particle is first introduced, to facilitate readers to better understand the research of the muon anomalous magnetic moment and the research methods in high-precision frontiers.