[en] The purpose of the present lectures is to carry through the methods and procedures necessary for a meaningful spectroscopy of the heaviest few-electron ions in relation to present theories. Results achieved so far in accelerator-based X-ray experiments are highlighted with emphasis on recent developments on heavy-ion storage rings. Starting with a brief account of the basics of one-electron ions, the motivation for doing X-ray spectroscopy of the simplest atomic systems with a high nuclear charge is given. In section 2 X-ray instrumentation and techniques are discussed including the precautions necessary when dealing with fast-beam sources. Peculiarities of heavy-ion storage rings are investigated in section 3 with regard to their use for spectroscopy. In section 4 are discussed results obtained so far on the measurement of the Lamb shift in very heavy ions. Section 5 gives some perspectives for the near future. (orig.)