Relativistic interactions with matter involving heavy high-Z ions provide a unique testing ground for our understanding of quantum electrodynamics and correlation in the non-perturbative regime as well as of elementary atomic processes mediated by ultrafast electromagnetic interactions. For this realm of physics, the future international accelerator Facility for Antiproton and Ion Research (FAIR) has key features that offer a range of novel challenging research opportunities. In this talk, I will also review recent experimental results for atomic, quantum and fundamental research obtained at the already existing ion storage and trapping facilities. Examples include e.g. laser spectroscopy exploiting the large Doppler boost associated with relativistic ions as well as precision x-ray, laser and di-electronic recombination spectroscopy. Finally, experiments at the border between atomic and nuclear physics will be addressed in addition with emphasis on rare nuclear decay modes only possible at high atomic charge states.