With the increasing growth of internet-of-things (IoT) devices, effective computation performance has become a critical issue. Many services provided by IoT devices (e.g., augmented reality, location-tracking, traffic systems, and autonomous driving) require intensive real-time data processing, which demands powerful computational resources. Mobile edge computing (MEC) has been introduced to effectively handle this problem reliably over the internet. The inclusion of a MEC server allows computationally intensive tasks to be offloaded from IoT devices. However, communication overhead and delays are major drawbacks. With the advantages of high mobility and low cost, unmanned aerial vehicles (UAVs) can mitigate this issue by acting as MEC servers. The offloading decisions for such scenarios involve service latency, energy/power consumption, and execution delays. For this reason, this study reviews UAV-enabled MEC solutions in which offloading was the focus of research. We compare the algorithms qualitatively to assess features and performance. Finally, we discuss open issues and research challenges in terms of design and implementation.