The air-ground integrated sensing and communications (AG-ISAC) network, which consists of unmanned aerial vehicles (UAVs) and ground terrestrial networks, offers unique capabilities and demands special design techniques. In this article, we provide a review on AG-ISAC, by introducing UAVs as ``relay'' nodes for both communications and sensing to resolve the power and computation constraints on UAVs. We first introduce an AG-ISAC framework, including the system architecture and protocol. Four potential use cases are then discussed, with the analysis on the characteristics and merits of AG-ISAC networks. The research on several critical techniques for AG-ISAC is then discussed. Finally, we present our vision of the challenges and future research directions for AG-ISAC, to facilitate the advancement of the technology.