Adverse weather conditions such as haze, rain, and snow significantly degrade the quality of images and videos, posing serious challenges to intelligent transportation systems (ITS) that rely on visual input. These degradations affect critical applications including autonomous driving, traffic monitoring, and surveillance. This survey presents a comprehensive review of image and video restoration techniques developed to mitigate weather-induced visual impairments. We categorize existing approaches into traditional prior-based methods and modern data-driven models, including CNNs, transformers, diffusion models, and emerging vision-language models (VLMs). Restoration strategies are further classified based on their scope: single-task models, multi-task/multi-weather systems, and all-in-one frameworks capable of handling diverse degradations. In addition, we discuss day and night time restoration challenges, benchmark datasets, and evaluation protocols. The survey concludes with an in-depth discussion on limitations in current research and outlines future directions such as mixed/compound-degradation restoration, real-time deployment, and agentic AI frameworks. This work aims to serve as a valuable reference for advancing weather-resilient vision systems in smart transportation environments. Lastly, to stay current with rapid advancements in this field, we will maintain regular updates of the latest relevant papers and their open-source implementations at https://github.com/ChaudharyUPES/A-comprehensive-review-on-Multi-weather-restoration
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