Unmanned aerial vehicle (UAV) swarm enabled edge computing is envisioned to be promising in the sixth generation wireless communication networks due to their wide application sensories and flexible deployment. However, most of the existing works focus on edge computing enabled by a single or a small scale UAVs, which are very different from UAV swarm-enabled edge computing. In order to facilitate the practical applications of UAV swarm-enabled edge computing, the state of the art research is presented in this article. The potential applications, architectures and implementation considerations are illustrated. Moreover, the promising enabling technologies for UAV swarm-enabled edge computing are discussed. Furthermore, we outline challenges and open issues in order to shed light on the future research directions.