For many years, atomic lifetime measurements on multiply-charged ions have been done almost exclusively by beam-foil spectroscopy. For low ion charges, however, spin-changing "intercombination" transitions have a rate that renders them too slow for traditional fast-beam techniques. Here ion traps and fast-ion beams have been combined in the concept of heavy-ion storage rings. These devices have permitted not only an extension of intercombination lifetime measurements down to singly charged ions, but they also facilitated similar measurements on electric-dipole forbidden transitions. The electron-beam ion trap (EBIT) complements the storage-ring work for work on highly charged ions. Achievements, technical issues, and prospects are outlined. PACS Nos.: 32.70Cs, 32.30Jc, 34.50Fa