Air lasing is a concept that refers to remote no-cavity (mirrorless) optical amplification in ambient air with the air constituents as the gain media.Due to the high potential of air lasing in view of applications in atmospheric sensing,a variety of pumping schemes have been proposed so far for building up population-inverted gain media in air and producing forward and/or backward directional lasing emissions.This review paper presents an overview of recent advances in the experimental observations and physical understanding of air lasing in various pumping schemes of air molecules by intense laser fields.Special emphasis is given to the strong-field-induced N2+ air lasing,the mechanism of which is currently still in a hot debate.