The modeling of atmospheric clouds is one of the crucial elements in the natural phenomena visualization system. Over the years, a wide range of approaches has been proposed on this topic to deal with the challenging issues associated with visual realism and performance. However, the lack of recent review papers on the atmospheric cloud modeling methods available in computer graphics makes it difficult for researchers and practitioners to understand and choose the well-suited solutions for developing the atmospheric cloud visualization system. Hence, we conducted a comprehensive review to identify, analyze, classify, and summarize the existing atmospheric cloud modeling solutions. We selected 113 research studies from recognizable data sources and analyzed the research trends on this topic. We defined a taxonomy by categorizing the atmospheric cloud modeling methods based on the methods' similar characteristics and summarized each of the particular methods. Finally, we underlined several research issues and directions for potential future work. The review results provide an overview and general picture of the atmospheric cloud modeling methods that would be beneficial for researchers and practitioners.