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Advances in imaging and display engineering have given rise to new and improved image and videoapplications that aim to maximize visual quality under given resource constraints (e.g., power, bandwidth).Because the human visual system is an imperfect sensor, the images/videos can be represented in a mathematicallylossy fashion but with enough fidelity that the losses are visually imperceptible—commonly termed“visually lossless.” Although a great deal of research has focused on gaining a better understanding ofthe limits of human vision when viewing natural images/video, a universally or even largely accepted definitionof visually lossless remains elusive. Differences in testing methodologies, research objectives, and targetapplications have led to multiple ad-hoc definitions that are often difficult to compare to or otherwise employ inother settings. We present a compendium of technical experiments relating to both vision science and visualquality testing that together explore the research and business perspectives of visually lossless image quality,as well as review recent scientific advances. Together, the studies presented in this paper suggest that a singledefinition of visually lossless quality might not be appropriate; rather, a better goal would be to establish varyinglevels of visually lossless quality that can be quantified in terms of the testing paradigm., Copyright (2018) Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.