Nowadays, 360° video/image has been increasingly popular and drawn great attention. The spherical viewing range of 360° video/image accounts for huge data, which pose the challenges to 360° video/image processing in solving the bottleneck of storage, transmission, etc. Accordingly, the recent years have witnessed the explosive emergence of works on 360° video/image processing. In this article, we review the state-of-the-art works on 360° video/image processing from the aspects of perception, assessment and compression. First, this article reviews both datasets and visual attention modelling approaches for 360° video/image. Second, we survey the related works on both subjective and objective visual quality assessment (VQA) of 360° video/image. Third, we overview the compression approaches for 360° video/image, which either utilize the spherical characteristics or visual attention models. Finally, we summarize this overview article and outlook the future research trends on 360° video/image processing.