Precision studies of fundamental atomic structure with heaviest few-electron ions

One- and few-electron ions traditionally serve as an important testing ground for fundamental atomic structure theories and for the effects of QED, relativity and electron correlation. In the domain of high nuclear charges, new opportunities open up for precise testing and consolidating of the present understanding of the atomic structure in the regime of extreme electromagnetic fields. In this review, the current progress in experimental investigations of the heaviest H- and He-like systems at GSI Darmstadt is presented together with the planned future developments.