The study during the past twenty years on the Tibetan Plateau driven air-pump (TP-SHAP) and its impacts on the Asian summer monsoon is reviewed. The impact mechanisms are summarized from the perspective of energy (θ), potential vorticity-diabatic heating (PV-Q), and angular momentum conservation (AMC) constraint. It is demonstrated that the surface sensible heating on the plateau's slopes plays a significant role in changing the energy of the air parcel moving towards the plateau and generating its vertical pumping. The PV forcing induced by the TP-SHAP generates a strong and vast cyclonic circulation surrounding the plateau in the lower troposphere, which transports abundant water vapor from the sea to the land to feed the continental monsoon rainfall. Through changing the thermal and circulation structure over the TP, the plateau surface sensible heating also produces minimum absolute vorticity and potential vorticity in the upper troposphere in the subtropics, and induces a monsoonal type meridional circulation under the constraint of angular momentum conservation. It provides a favorable large-scale ascending background for the monsoon development over the vast Asian summer monsoon area. A brief comment on the recent discussion of the TP impact on Asian monsoon formation is provided as well, and an outlook on future study is given at the end.