Abstract: With the rapid development of mobile Internet and video processing technologies， virtual reality has become an essential component of modern information society， with widespread applications in recent years. Omnidirectional video is a key medium in virtual reality， allowing viewers wearing headsets to adjust their viewports and explore content of interest. In terms of the field of view， unlike conventional planar videos， omnidirectional videos provide 360° coverage and impose higher requirements on resolutions and frame rates， producing substantial amounts of data. In bandwidth-constrained environments， the transmission and storage of massive omnidirectional videos require reducing data redundancy， making omnidirectional video compression a critical research area. However， the compression process inevitably introduces distortions. Furthermore， in real-world video processing pipelines， multiple types of distortions are further compounded by operations such as editing and transcoding. These compounded distortions degrade the quality of experience and constrain the development of downstream video processing tasks. Quality assessment techniques provide effective evaluation metrics and optimization objectives for quality enhancement technologies. This paper focuses on key technologies for omnidirectional video compression and quality assessment. First， we review both traditional and deep learning methods for omnidirectional video compression， including the latest advancements in neural omnidirectional video codecs， as well as commonly used datasets and evaluation metrics. Next， we review subjective and objective quality assessment methods for omnidirectional videos. For subjective quality assessment， we review experimental protocols and datasets involving synthetic and real-world distortions. For objective quality assessment， we provide a detailed review of no-reference quality assessment methods， including deep learning models designed for real-world distortions. Finally， we summarize the core technologies in omnidirectional video compression and quality assessment and discuss future directions to promote the application and development of omnidirectional video processing technologies.