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Unmanned aerial vehicles (UAVs) have been introduced into wireless communication systems to provide high-quality services and enhanced coverage due to their high mobility. In this article, we study a UAV-assisted mobile-edge computing (MEC) system in which a moving UAV equipped with computing resources is employed to help user devices (UDs) compute their tasks. The computing tasks of each UD can be divided into two parts: one portion is processed locally and the remaining portion is offloaded to the UAV for computing. Offloading is enabled by uplink and downlink communications between UDs and the UAV. On this basis, two types of access modes are considered, namely, nonorthogonal and orthogonal multiple access. For both access modes, we formulate new optimization problems to minimize the weighted-sum energy consumption of the UAV and UDs by jointly optimizing the UAV trajectory …