Nuclear theories span a broad range of refinement from the liquid drop model to highly involved ab initio theories. In the middle of that scale lie selfconsistent models, also known as nuclear density functional theory (DFT). They constitute presently the best compromise between expense and benefit. The talk will focus on this class of models.
With the help of some empirical input for a good calibration, nuclear DFT aims at a universal description of nuclei and nuclear matter. The goal is to cover as many observables as possible. Nuclear radii are here, besides binding energies, the most prominent observables which had been heavily used for model development since the early days of nuclear DFT. In the meantime, experimental access to nuclear radii has dramatically improved concerning the range of available nuclei as well as precision. These new data puts the theory to the test and, at the same time, provides excellent material for their improvement. The talk will review the last decades progress in describing nuclear radii and the yet open ends.