Atomic lifetime measurements yield information on atomic wavefunctions that supplements the data from atomic energy levels, but is more sensitive to details of the radial wavefunctions. Transition rates of intercombination (spin-changing) and electric-dipole forbidden transitions are of interest also for applications in plasma diagnostics and astrophysics. Earlier lifetime measurements of low-charge state ions in radiofrequency, electrostatic and Penning ion traps have recently been supplemented and in some cases superseded by experiments on electron-beam ion traps (EBIT) and heavy-ion storage rings. Several of these measurements of lifetimes in the range from 10 μs to 500 ms have reached uncertainties of better than 0.5% and challenge theory. Typical features of ion trap experiments, performance problems and technical developments are reviewed, and likely routes of further progress are outlined.