An overview is presented of laser spectroscopy experiments with cold, trapped, highly charged ions, which will be performed at the HITRAP facility at GSI in Darmstadt (Germany). These high-resolution measurements of ground-state hyperfine splittings will be three orders of magnitude more precise than previous measurements. Moreover, from a comparison of measurements of the hyperfine splittings in hydrogen-like and lithium-like ions of the same isotope, QED effects at high electromagnetic fields can be determined within a few percent. Several candidate ions suited for these laser spectroscopy studies are presented.PACS Nos.: 12.20.Fv, 21.10.Ky, 32.10.Fn, 32.30.–r