With proliferation of smart devices and wireless applications, the recent few years have witnessed data surge. These massive data needs to be stored, transmitted, and processed in time to exploit their value for decision making. Conventional cloud computing requires transmission of massive amount of data in and out of core network, which can lead to longer service latency and potential traffic congestion. As a new platform, mobile edge computing (MEC) moves computation and storage resources to edge network in proximity to the data source. With MEC, data can be processed locally, and thus mitigate issues of latency and congestion. However, it is very challenging to reap the benefits of MEC everywhere due to geographic constraints, expensive deployment cost, and immoveable base stations. Because of easy deployment and high mobility of unmanned aerial vehicles (UAVs), air-ground integrated mobile edge networks (AGMEN) is proposed, where UAVs are employed to assist the MEC network. Such an AGMEN expects to provide MEC services ubiquitously and reliably. In this article, we first introduce the characteristics and components of UAV. Then, we will review the applications, key challenges, and current research technologies of AGMEN, from perspectives of communication, computation, and caching, respectively. Finally, we will discuss some essential research directions for AGMEN.