The Asian monsoon is the most significant component of the global climate system. During recent two decades, a more and more efforts have been made to study the Asian monsoon. A substantial achievement has been made in basic physical processes, predictability and prediction since the MONEX of [1978][1979]. The major advance in our new understanding of the variability of the Asian summer monsoon has been highlighted in this paper. The present paper is structured with four parts. The first part is the introduction, indicating the new regional division of the Asian monsoon system and significant events of the history of the Asian monsoon research. The second part discusses the annual cycle and seasonal march of the Asian monsoon as the mean state, with a special emphasis on the onset, propagation, active-break cycle and withdrawal of the Asian summer monsoon. The process and mechanism of the earliest onset of the Asian summer monsoon which takes place in the near-equatorial East Indian ocean-central and southern Indochina Peninsula have been well documented. The third part deals with the multiple scale variability of the Asian summer monsoon, including the intraseasonal, interannual and inter-decadal variability. Their dominant modes such as 10-20 day and 30-60 day oscillations for the intraseasonal variability, the Tropospheric Biennial Oscillation (TBO), the Indian Ocean Dippole Mode (IODM) and teleconnection patterns for interannual variability and the 60-year oscillation for the inter-decadal variability, as well as related SST-monsoon relationship and land-monsoon relationship have been discussed in more details. The fourth part is the conclusion, summarizing the major findings and proposing future work.