Quantifying the perceptual difference between original and reproduced (and inevitably modified) color images is currently a key research challenge in the field of color imaging. Such information can be extremely valuable for instance in the development of new equipment and algorithms for color reproduction. While in many research areas it is common practice to obtain quantitative quality information by the use of perceptual tests, in which the judgments of several human observers are being collected and carefully analyzed statistically, this approach has serious limitations for practical use, in particular because of the time consumption. Motivated by this, and aided by the ever increasing available knowledge about the mechanisms of the human visual system, the quest for perceptual color image quality metrics that can adequately predict human quality judgments of complex images, has been on for several decades. However, unfortunately, the Holy Grail is yet to be found. The current paper outlines the state of the art of this field, including benchmarking of existing metrics, presents recent research, and proposes promising areas for further work. Aspects that are covered in particular include new models and metrics for color image quality, and new frameworks for using the metrics to improve color image representation and reproduction algorithms.