The ever increasing mobile data demands have posed significant challenges in the current radio access networks, while the emerging computation- heavy Internet of Things applications with varied requirements demand more flexibility and resilience from the cloud/edge computing architecture. In this article, to address the issues, we propose a novel air-ground integrated mobile edge network (AGMEN), where UAVs are flexibly deployed and scheduled, and assist the communication, caching, and computing of the edge network. Specifically, we present the detailed architecture of AGMEN, and investigate the benefits and application scenarios of drone cells, and UAV-assisted edge caching and computing. Furthermore, the challenging issues in AGMEN are discussed, and potential research directions are highlighted.