In this paper, we discuss the radioactive decay of highly charged ions. There are several motivations for performing this kind of research. One of them is that stellar nucleosynthesis proceeds at high temperatures and therefore the involved atoms are highly ionized. Highly charged ions also offer the possibility of addressing the decay of well-defined quantum-mechanical systems such as, for example, one-electron ions, where all the interactions with other electrons are excluded. These studies can be performed solely at ion storage rings or ion traps, where the high atomic charge states can be preserved for extended periods of time. Although we have focused on experiments conducted at the storage ring ESR of GSI, we have tried to describe the general requirements for such experiments.
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