Next‐generation wireless communication networks, in particular, the densified 5G will bring many developments to the existing telecommunications industry. The key benefits will be the higher throughput and very low latency. In this context, the usage of unmanned aerial vehicle (UAV) is becoming a feasible option for deploying 5G services on demand. At the same time, the immense bandwidth potential of mmWave has strengthened its performance in radio communication. In this article, we provide a consolidated synthesis on the role of UAVs and mmWave in 5G, emphasis on recent developments and challenges. The review focuses on UAV relay architectures, identifies the relevant problems and limitations in the deployment of UAVs using mmWave in both access and backhaul links simultaneously. There is a critical analysis of the optimum placement of the UAVs as a relay with a focus on the mmWave band. The distinctive rich characteristics of the mmWave propagation and scattering are presented. We also synthesis mmWave path loss models. Then, the scope of artificial intelligence and machine learning techniques as an efficient solution for combating the dynamic and complex nature of UAV‐based cellular communication networks are discussed. In the end, security and privacy issues in UAV‐based cellular network are spotlighted. It is believed that the literature discussed, and the findings reached in this article are of significant importance to researchers, application engineers and decision‐makers in the designing and deployment of UAV‐supported 5G network.