Image quality assessment (IQA) aims to measure the consistency between an objective algorithm output and a subjective perception measurement. This article focuses on this complex relationship in the context of color image scenarios—color image quality assessment (CIQA). This review systematically investigates CIQA applications in image compression, processing optimization, and domain-specific scenarios, analyzes benchmark datasets and assessment metrics, and categorizes CIQA algorithms into full-reference (FR), reduced-reference (RR) and no-reference (NR) methods. In this study, color images are evaluated using a newly developed CIQA framework. Focusing on FR and NR methods, FR methods leverage reference images with machine learning, visual perception models, and mathematical frameworks, while NR methods utilize distortion-only features through feature fusion and extraction techniques. Specialized CIQA algorithms are developed for robotics, low-light, and underwater imaging. Despite progress, challenges remain in cross-domain adaptability, generalization, and contextualized assessment. Future directions may include prototype-based cross-domain adaptation, fidelity–structure balancing, spatiotemporal consistency integration, and CIQA–restoration synergy to meet emerging demands.