The increase in air missions, coupled with the rapid developing of unmanned aerial vehicles, promotes the development in network oriented airborne communication. As an important hub to connect the air communication satellite networks and terrestrial networks, airborne network has many new features (which are different from the wireless mobile network), such as large-scale three-dimensional distribution sparse scene, long transmission ranges, mobile predictable trajectory, high-speed mobile, high dynamic topology, and clustering structure. Meanwhile, it faces new challenges in its architecture and protocol stack design, thus becomes a hot topic in academia and industry. In this paper, the architecture and characteristics of airborne network are first introduced. Then a systematic summary is provided on the research progress of three important topics: medium access control protocols, routing protocols and transmission control protocols. Finally, problems in current research and future research directions of this area are discussed.