Unmanned Aerial Vehicles (UAVs) offer agile, secure and efficient solutions for communication relay networks. However, their modeling and control are challenging, and the mismatch between simulations and actual conditions limits real-world deployment. Moreover, improving situational awareness is essential. Several studies proposed integrating the operation of UAVs with immersive digital technologies such as Digital Twin (DT) and Extended Reality (XR) to overcome these challenges. This paper provides a comprehensive overview of the latest research and developments involving immersive digital technologies for UAVs. We explore the use of Machine Learning (ML) techniques, particularly Deep Reinforcement Learning (DRL), to improve the capabilities of DT for UAV systems. We provide discussion, identify key research gaps, and propose countermeasures based on Generative AI (GAI), emphasizing the significant role of AI in advancing DT technology for UAVs. Furthermore, we review the literature, provide discussion, and examine how the XR technology can transform UAV operations with the support of GAI, and explore its practical challenges. Finally, we propose future research directions to further develop the application of immersive digital technologies for UAV operation.