Network slicing is a promising approach supporting various Internet of Everything applications with diverse and differential requirements. To implement flexible and efficient network slices, unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) is deployed to leverage aerial and ground segments, which provides multi-dimensional resources involving various hardware devices and facilities (e.g., UAVs, edge servers, and network devices). Such a complex and hierarchical structure requires an efficient framework to orchestrate and control network slices while considering specific and unique characteristics of the UAVs deployed in the system. In this work, we propose a new systematic architecture named slicing-based software-defined MEC in the air, where virtual resource blocks provided by UAVs and edge devices are ubiquitously integrated into network slices to offer customized UAV-enabled MEC services by software-defined technologies. Then we identify three slicing patterns implemented by organized embeddings of UAVs, which are full slicing, partial slicing, and separated slicing patterns. Based on the proposed slicing-based software-defined scheme, two potential application scenarios and some open issues are discussed. In particular, we develop a Lyapunov optimization-based offloading algorithm for the efficient selection of resource slices. Finally, some simulation results are presented to depict the effectiveness of the proposed scheme. © 2002-2012 IEEE.