One of the most promising approaches to address the mismatch between computation- intensive applications and computation-limited end devices is multi-access edge computing (MEC). To overcome the rapid increase in traffic volume and offload the traffic from macrocells, a massive number of small cells have been deployed, so-called heterogeneous networks (HetNets). Strongly motivated by the close integration of MEC and HetNets, in this paper, we propose an envisioned architecture of MEC-empowered HetNets, where both wireless and wired backhaul solutions are supported, flying base stations (BSs) can be equipped with MEC servers, and mobile users (MUs) need both communication and computation resources for their computationally heavy tasks. Subsequently, we provide the research progress summary of task offloading and resource allocation in the proposed MEC-empowered unmanned aerial vehicle (UAV)-assisted heterogeneous networks. We complete this article by spotlighting key challenges and open future directives for researches.