With the rapid expansion of the Internet of Things (IoT), the demand for computational resources continues to soar, necessitating innovative solutions to address the needs of resource-constrained IoT users. Mobile edge computing (MEC) emerges as a promising remedy, mitigating the strain imposed by resource-intensive mobile applications. Concurrently, leveraging unmanned aerial vehicles (UAVs) as aerial platforms presents an enticing opportunity to enhance connectivity in wireless networks, owing to their on-demand deployment capabilities, high cruising altitudes, and maneuverability in three-dimensional space. This paper presents a comprehensive examination of UAV-enabled aerial MEC, elucidating its advantages, challenges, and recent advancements across various domains. Topics explored include joint optimization of UAV trajectory, computation offloading, and resource allocation, UAV deployment strategies, task scheduling, load balancing, interplay with other technologies, and machine learning-driven optimizations. Additionally, the paper outlines key avenues for future research endeavors.