Isotope Shifts of short-lived isotopes have been measured in the majority of the elements. To extract reliable charge radii from them, the canonical method is to calibrate two atomic parameters using three or more radii measured independently with stable nuclei. This "King Plot" procedure is applicable in about a quarter of the measured cases. The other cases require input from atomic theory. Odd elements pose a significant challenge in this regard. Only recently, and only in a few cases, has atomic theory caught up with experiment. In this talk I will present new many-body calculations which enable the first nuclear-model-independent extraction of the charge radii of Na, as well as improved radii for Mg. I will review the current status and implications over the periodic table.