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Images are a convenient way for humans to obtain information and knowledge, but they are often destroyed throughout the collection or distribution process. Therefore, image processing evolves as the need arises, and color image processing is a broad and active field. A color image includes three distinct but closely related channels (red, green, and blue (RGB)). Compared to directly expressing color images as vectors or matrices, the quaternion representation offers an effective alternative. There are several papers and works on this subject, as well as numerous definitions, hypotheses, and methodologies. Our observations indicate that the quaternion representation method is effective, and models and methods based on it have rapidly developed. Hence, the purpose of this paper is to review and categorize past methods, as well as study their efficacy and computational examples. We hope that this research will be helpful to academics interested in quaternion representation.