Unmanned Aerial Vehicles (UAVs) provide agile and safe solutions to communication relay networks, offering improved throughput. However, their modeling and control present challenges, and real-world deployment is hindered by the gap between simulation and reality. Moreover, enhancing situational awareness is critical. Several works in the literature proposed integrating UAV operation with immersive digital technologies, such as Digital Twin (DT) and Extended Reality (XR), to address these challenges. This paper provides a comprehensive overview of current research and developments involving immersive digital technologies for UAVs, including the latest advancements and emerging trends. We also explore the integration of DT and XR with Artificial Intelligence (AI) algorithms to create more intelligent, adaptive, and responsive UAV systems. Finally, we provide discussions, identify gaps in current research, and suggest future directions for studying the application of immersive technologies in UAVs, fostering further innovation and development in this field. We envision the fusion of DTs with XR will transform how UAVs operate, offering tools that enhance visualization, improve decision-making, and enable effective collaboration.