The facet-dependent adsorption of CO on oxidized and reduced CeO₂ single crystal surfaces is reviewed, with emphasis on the effect of CO coverage and the ability of state-of-the-art quantum-mechanical methods to provide reliable energies and an accurate description of the IR vibrational frequency of CO. Comparison with detailed, high-resolution experimental IRRAS data performed on single crystal samples allows the assignment of the different CO vibrational bands observed on all three low-index ceria surfaces. Good agreement is achieved with the hybrid DFT approach with the HSE06 functional and with saturation coverage. It is shown that CO is very sensitive to the structure of cerium oxide surfaces and to the presence of oxygen vacancies. The combined theoretical-experimental approach offers new opportunities for a better characterization of ceria nanoparticles and for unraveling changes occurring during reactions involving CO at higher pressures.