The origin of the Moon is a key issue for understanding the early evolution of the Earth-Moon system and the inner Solar System. Since the Apollo era, the giant impact hypothesis has remained one of the leading hypotheses for the origin of the Moon, but the broad isotopic similarities between Earth and Moon have also imposed important challenges on this model. In recent years, advances in high-precision isotopic analysis, progress in lunar sample chronology, and the return of samples by Chang'e-5 and Chang'e-6 missions have substantially improved our understanding of lunar formation, magma-ocean evolution, and late-stage volcanisms. This paper reviews recent progress in geochemistry, petrology, and isotopic geochronology, with emphasis on the giant-impact origin of the Moon, and the subsequent evolution of the lunar magma ocean. Current studies broadly support lunar formation within several tens to more than one hundred million years after Solar System formation, although significant disagreement remains among different isotopic systems and their interpretations. Samples returned by Chang'e-5 and Chang'e-6 extend known lunar volcanism to about 2.0 Ga and 2.8 Ga, respectively, and provide key constraints for improving the lunar crater chronology and understanding the thermal asymmetry between the nearside and farside.