We review the coronal visible and infrared lines, collecting previous observations, and comparing, whenever available, observed radiances with those predicted by various models: the quiet Sun, a moderately active Sun, and an active region as observed near the limb, around 1.1R$_{odot}$. We also model the off-limb radiances for the quiet Sun case. We used the most up-to-date atomic data in CHIANTI version 8. The comparison is satisfactory, in that all of the strong visible lines now have a firm identification. We revise several previous identifications and suggest some new ones. We also list the large number of observed lines for which we do not currently have atomic data, and therefore still await firm identifications. We also show that a significant number of coronal lines should be observable in the near-infrared region of the spectrum by the upcoming Daniel K. Inouye Solar Telescope (DKIST) and the AIR-Spec instrument, which observed the corona during the 2017 August 21 solar eclipse. We also briefly discuss the many potential spectroscopic diagnostics available to the visible and infrared, with particular emphasis on measurements of electron densities and chemical abundances. We briefly point out some of the potential diagnostics that could be available with the future infrared instrumentation that is being built for DKIST and planned for the Coronal Solar Magnetism Observatory (COSMO). Finally, we highlight the need for further improvements in the atomic data.
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