Over the past decade, the utilization of UAVs has witnessed significant growth, owing to their agility, rapid deployment, and maneuverability. In particular, the use of UAV-mounted 360-degree cameras to capture omnidirectional videos has enabled truly immersive viewing experiences with up to 6DoF. However, achieving this immersive experience necessitates encoding omnidirectional videos in high resolution, leading to increased bitrates. Consequently, new challenges arise in terms of latency, throughput, perceived quality, and energy consumption for real-time streaming of such content. This paper presents a comprehensive survey of research efforts in UAV-based immersive video streaming, benchmarks popular video encoding schemes, and identifies open research challenges. Initially, we review the literature on 360-degree video coding, packaging, and streaming, with a particular focus on standardization efforts to ensure interoperability of immersive video streaming devices and services. Subsequently, we provide a comprehensive review of research efforts focused on optimizing video streaming for timevarying UAV wireless channels. Additionally, we introduce a high resolution 360-degree video dataset captured from UAVs under different flying conditions. This dataset facilitates the evaluation of complexity and coding efficiency of software and hardware video encoders based on popular video coding standards and formats, including AVC/H.264, HEVC/H.265, VVC/H.266, VP9, and AV1. Our results demonstrate that HEVC achieves the best trade-off between coding efficiency and complexity through its hardware implementation, while AV1 format excels in coding efficiency through its software implementation, specifically using the libsvt-av1 encoder. Furthermore, we present a real testbed showcasing 360-degree video streaming over a UAV, enabling remote control of the drone via a 5G cellular network.