Geological climatic records and model simulations on the Asian summer monsoon climate change induced by insolation forcing of the Earth's precession are systematically reviewed in this paper.The presentation of the questions on the mechanism of the Asian monsoon evolution at the precession band,currently existing debates and future research directions are discussed.Since the early 1980s,more and more observed evidence and simulated results,especially the absolute-dated stalagmite records and orbital-scale transient model runs in the last few years,have indicated that the quasi-20ka period in the Quaternary monsoon climate change is caused by precession.However,debates still exist on the dynamic mechanism how precession affects the Asian monsoon.The "zero phase" hypothesis says that the Asian monsoon is merely controlled by summer insolation in the Northern Hemisphere(NH) while the "latent heat" hypothesis emphasizes the dominant effect of latent heat transport from the Southern Hemisphere(SH) besides the role of the northern insolation.The two hypotheses have separately been supported by some evidence.Although we are cognizant of the importance of northern solar radiation and the remote effect of southern insolation,it has still a long way to go before comprehensively understanding the evolutionary mechanism of the Asian monsoon.In view of the problems existing in present researches of monsoon-dominated climate change at the precession scale,we propose that studies on the environmental significance of geological monsoon proxies,feedback processes in the long-term transient simulations and intercomparisons between observations and modeling results should be strengthened in the future.