Highly charged radioactive ions can be stored for extended periods of time in storage rings which allows for precision measurements of their decay modes. The straightforward motivation for performing such studies is that fully ionised nuclei or few-electron ions can be viewed as clean quantum-mechanical systems, in which the interactions of the many electrons can be either excluded or treated precisely. Thus, the influence of the electron shell on the decay probability can be investigated. Another important motivation is stellar nucleosynthesis, which proceeds at high temperatures and the involved atoms are therefore highly ionised. Presented here is a compact review of the relevant experiments conducted at heavy-ion storage rings. Furthermore, we outline the perspectives for future experiments at new-generation storage-ring facilities.