Cold atmospheric-pressure plasma jet generates rich reactive species including reactive oxygen species and reactive nitrogen species with gas temperature close to or at room temperature, which is very attractive for applications such as plasma medicine. However, under one atmospheric pressure, due to the high electron-neutral particles collision frequency (10(11-12)/s), it is difficult to generate atmospheric pressure plasma while keeping the gas temperature close to or at room temperature. Furthermore, when air rather than noble gases is used as working gas, due to the low energy levels of rotational and vibrational states of nitrogen and oxygen, it becomes extremely challenging to generate cold atmospheric pressure air plasma jet (CAAP-J) with gas temperature close to or at room temperature. Fortunately, after decades of research, several CAAP-Js have been reported. In this review, the state-of-the-art of the development of CAAP-Js is presented. The CAAP-Js are grouped into six categories based on their electrode configuration. A brief discussion on each group of the CAAP-Js is presented. Moreover, the physics of CAAP-Js is discussed, including the dynamics, the striation phenomenon, the temporal behavior of plasma parameters, and the nonequilibrium characteristic of CAAP-Js. Furthermore, the measurements of the reactive species generated by CAAP-Js are briefly reviewed. Finally, discussions and perspective of future research on CAAP-Js are presented.</p>