Ultra-reliable low-latency communications (URLLCs) and the adoption of unmanned aerial vehicles (UAVs) for network coverage improvement have emerged as key enabling communication paradigms for the successful deployment of mobile communication services envisioned in both the fifth-generation (5G) and the sixth-generation (6G) networks. This paper provides a comprehensive survey about the current state-of-the-art (SoA) on UAV-enabled URLLC networks. The core idea is to highlight the main characteristics of this new network concept as well as its critical aspects. We first perform an overview of URLLC by illustrating the main features and related implementation chellenges. Subsequently, an indepth discussion on UAV-enabled networks is provided, with a special emphasis on how URLLCs and UAV communication can be classified as complementary paradigms. Finally, a comprehensive analysis and classification of the current research advancements on UAV-enabled URLLCs networks is carried out. This paper is concluded by pointing out some the open challenges and our visions related to future directions which should be undertaken in order to pave the way towards the practical implementation of this promising network architecture.