With the emergence of computation-intensive and delay-sensitive applications, such as face recognition, virtual reality, augmented reality, and Internet of Things (IoT) devices; Mobile Edge Computing (MEC) allows the IoT devices to offload their heavy computation tasks to nearby edge cloud network rather than to compute the tasks locally. Therefore, it helps to reduce the energy consumption and execution delay in the ground mobile users. Flying Unmanned Aerial Vehicles (UAVs) integrated with the MEC server play a key role in 5G and future wireless communication networks to provide spatial coverage and further computational services to the small, battery-powered and energy-constrained devices. The UAV-enabled MEC (U-MEC) system has flexible mobility and more computational capability compared to the terrestrial MEC network. They support line-of-sight (LoS) links with the users offloading their tasks to the UAVs. Hence, users can transmit more data without interference by mitigating small-scale fading and shadowing effects. UAVs resources and flight time are very limited due to size, weight, and power (SWaP) constraints. Therefore, energy-aware communication and computation resources are allocated in order to minimize energy consumption.In this paper, a brief survey on U-MEC networks is presented. It includes the brief introduction regarding UAVs and MEC technology. The basic terminologies and architectures used in U-MEC networks are also defined. Moreover, mobile edge computation offloading working, different access schemes used during computation offloading technique are explained. Resources that are needed to be optimized in U-MEC systems are depicted with different optimization problem, and solution types. Furthermore, to guide future work in this area of research, future research directions are outlined. At the end, challenges and open issues in this domain are also summarized.