The availability of high intensity, high quality beams of highly charged ions has started a new application for laser spectroscopy. High resolution spectroscopy can now be applied to a study of hydrogen-like atomic states in heavy elements. In principal, this will allow a determination of the hyperfine splitting with an accuracy in the 10^-6-range or better. Presently this exceeds the limits given by the uncertainties of the nuclear quantities, especially the distribution of the nuclear magnetization in the nucleus. Since the new approach can be applied to a family of test cases, it can provide a wide experimental basis for the separation of nuclear and QED effects. This is especially true since measurements of the hyperfine splitting have now also been performed at the Super-EBIT ion trap. For the determination of nuclear parameters it will be of benefit to measure more candidates close to the doubly magic ²⁰⁸Pb. In such systems theoretical efforts to clarify details of the nuclear structure and of the interaction between the nucleus and the electron can be expected to even surpass the present experimental accuracy.