As the Internet of Things (IoT) ecosystem evolves, innovative applications with stringent demands with respect to latency will emerge. To handle computation-intensive tasks in a timely manner, data offloading to Mobile Edge Computing (MEC) servers has been suggested. On the other hand, prospective IoT networks are expected to include Unmanned Aerial Vehicles (UAVs) to enhance coverage and connectivity, while retaining reliable communication links with ground nodes in urban, suburban, and rural terrain. Nevertheless, the evolution of UAV-aided MEC-enabled IoT presupposes the mitigation of security threats through the implementation of efficient and robust countermeasures. As UAVs inherently have certain limitations in terms of energy, computational, and memory resources, designing lightweight security solutions is required. This paper provides an overview of the UAV-aided MEC-enabled IoT and a detailed presentation of use cases and application scenarios, where security is of utmost importance. Subsequently, up-to-date research works on security solutions for the UAV-aided MEC-enabled IoT are comprehensively presented. To this end, the adoption of information-theoretic techniques that ensure adequate Physical-Layer Security (PLS) is discussed along with sophisticated security approaches based on emerging technologies, such as Blockchain and Machine Learning (ML). In addition, research studies on software-and hardware-based methods for the identification and authentication of network nodes are presented. Finally, this paper provides future perspectives in this research domain, stimulating further work.INDEX TERMS Blockchain, Internet of Things (IoT), Machine Learning (ML), Mobile Edge Computing (MEC), Physical-Layer Security (PLS), Unmanned Aerial Vehicle (UAV).