The Sun's atmosphere increases in temperature from 6000 degrees at the surface to over a million degrees at heights of a few thousand kilometers. This surprising temperature increase is still an active area of scientific study, but is generally thought to be driven by the dynamics of the Sun's magnetic field. The combination of a 2-to-3 order of magnitude temperature range and a low plasma density makes the solar atmosphere perhaps the best natural laboratory for the study of ionized atoms. Atomic transitions at ultraviolet (UV) and X-ray wavelength regions generally show no optical depth effects, and the lines are not subject to the interstellar absorption that affects astronomical sources. Here I highlight the importance of atomic data to modeling UV and X-ray solar spectra, with a particular focus on the CHIANTI atomic database. Atomic data needs and problems are discussed and future solar mission concepts presented.