Studies of the multi-scale climate variability of the Asian monsoon are essential to an advanced understanding of the physical processes of the global climate system. In this paper, the progress achieved in this field is systematically reviewed, with a focus on the past several years. The achievements are summarized into the following topics: (1) the onset of the South China Sea summer monsoon; (2) the East Asian summer monsoon; (3) the East Asian winter monsoon; and (4) the Indian summer monsoon. Specifically, new results are highlighted, including the advanced or delayed local monsoon onset tending to be synchronized over the Arabian Sea, Bay of Bengal, Indochina Peninsula, and South China Sea; the basic features of the record-breaking mei-yu in 2020, which have been extensively investigated with an emphasis on the role of multi-scale processes; the recovery of the East Asian winter monsoon intensity after the early 2000s in the presence of continuing greenhouse gas emissions, which is believed to have been dominated by internal climate variability (mostly the Arctic Oscillation); and the accelerated warming over South Asia, which exceeded the tropical Indian Ocean warming, is considered to be the main driver of the Indian summer monsoon rainfall recovery since 1999. A brief summary is provided in the final section along with some further discussion on future research directions regarding our understanding of the Asian monsoon variability.