Asian summer monsoon variability controls water resources, floods, droughts, and climate risks for densely populated regions, yet its multiscale behavior remains difficult to understand and predict because it is shaped by strongly coupled land, ocean, atmosphere, cryosphere, and topographic processes. This report synthesizes recent modeling studies that use potential-vorticity-based diagnostics, sensitivity experiments, hindcast simulations, and large-ensemble analyses to clarify how external forcings and internal feedbacks regulate Asian monsoon variability from subseasonal to interdecadal time scales. The main conclusion is that Tibetan Plateau surface potential vorticity provides a more physically integrated measure of plateau forcing than sensible heat alone, because it combines terrain, near-surface vorticity, and land–air thermal contrast, and its seasonal evolution is consistent with the development of Asian summer monsoon rainfall. Numerical experiments further show that Asian orography and plateau thermodynamic forcing substantially modulate monsoon precipitation and circulation, with coupled air–sea interactions amplifying or compensating model responses depending on region and configuration. Spring Tibetan Plateau forcing can be relayed into summer through both soil-temperature memory over the plateau and sea-surface-temperature memory over the western Pacific, thereby producing subseasonal precipitation anomalies over East Asia. At the extended-range scale, correcting subdaily thermal and dynamical perturbations over the plateau can improve East Asian precipitation forecasts, especially beyond two weeks in years with strong plateau forcing. The ocean also exerts crucial control. Seasonal SST modes, including ENSO, Indian Ocean Basin warming, tropical Atlantic variability, and western North Pacific SST anomalies, provide month-to-year precursors for persistent extreme precipitation over China by strengthening moisture transport and vertical motion. On longer time scales, Arctic sea ice loss and SST warming alter the East Asian summer monsoon trend through changes in Rossby wave propagation, meridional thermal contrast, and subtropical circulation. Together, these studies demonstrate that realistic simulation and prediction of Asian monsoon variability require an integrated land–ocean–atmosphere framework.