This study investigates the different aspects of multimedia computing in Video Synthetic Aperture Radar (Video-SAR) as a new mode of radar imaging for real-time remote sensing and surveillance. This research also considers new suggestions in the systematic design, research taxonomy, and future trends of radar data processing. Despite the conventional modes of SAR imaging, Video-SAR can generate video sequences to obtain online monitoring and green surveillance throughout the day and night (regardless of light sources) in all weathers. First, an introduction to Video-SAR is presented. Then, some specific properties of this imaging mode are reviewed. Particularly, this research covers one of the most important aspects of the Video-SAR systems, namely, the systematic design requirements, and also some new types of visual distortions which are different from the distortions, artifacts and noises observed in the conventional imaging radar. In addition, some topics on the general features and high-performance computing of Video-SAR towards radar communications through Unmanned Aerial Vehicle (UAV) platforms, Internet of Multimedia Things (IoMT), Video-SAR data processing issues, and real-world applications are investigated.