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X-ray spectroscopy of highly charged heavy ions is an important tool for the investigation of many topics in atomic physics. Such highly charged ions, in particular hydrogen-like uranium, are investigated at heavy ion storage rings, where high charge states can be produced in large quantities, stored for long times and cooled to low momentum spread of the ion beam. One prominent example is the determination of the 1s Lamb Shift in hydrogen-like heavy ions, which has been investigated at the Experimental Storage Ring (ESR) at the GSI Helmholtz Centre for Heavy Ion Research. Due to the large electron binding energies, the energies of the corresponding photon transitions are located in the X-ray regime. To determine the transition energies with high accuracy, highly resolving X-ray spectrometers are needed. One concept of such spectrometers is the concept of microcalorimeters, which, in contrast to semiconductor detectors, uses the detection of heat rather than charge to detect energy. Such detectors have been developed and successfully applied in experiments at the ESR. For experiments at the Facility for Antiproton and Ion Research (FAIR), the Stored Particles and Atoms Collaboration (SPARC) pursues the development of new microcalorimeter concepts and larger detector arrays. Next to fundamental investigations on quantum electrodynamics such as the 1s Lamb Shift or electron–electron interactions in two- and three-electron systems, X-ray spectroscopy may be extended towards nuclear physics investigations like the determination of nuclear charge radii.