Autonomous flight for UAVs relies on visual information for avoiding obstacles and ensuring safe collision-free flight. In addition to visual clues, safe UAVs often need connectivity with the ground station. In this article, we study the synergies between vision and communications for edge-computing-enabled UAV flight. By proposing a framework of edge computing assisted autonomous flight (ECAAF), we illustrate that vision and communications can interact with and assist each other with the aid of edge computing and offloading, and further speed up UAV mission completion. ECAAF consists of three functionalities that are discussed in detail: edge computing for 3D map acquisition, radio map construction from the 3D map, and online trajectory planning. During ECAAF, the interactions of communication capacity, video offloading, 3D map quality, and channel state of the trajectory form a positive feedback loop. Simulation results verify that the proposed method can improve mission performance by enhancing connectivity. Finally, we conclude with some future research directions.