Precision measurements with non-laser-cooled trapped ions

20 pages; International audience; Ion trapping has been applied to many different kinds of high-precision measurements. While applications such as optical spectroscopy and optical frequency standards require laser cooling of the trapped ions, this tutorial review concentrates on how a very high precision can be obtained in experiments with non-laser-cooled ions. Two specific topics are addressed: the first one is ultra-high-resolution mass spectrometry and $g$-factor measurements in Penning traps, and the second one is microwave spectroscopy on large ion ensembles in radiofrequency traps with applications to frequency standards. In both areas, the main motivations and basic experimental techniques are presented. Selected experimental results are described, highlighting the modern refinements of experimental methods which have allowed to reduce or eliminate the main systematic effects and improve the accuracy. Finally, future prospects are briefly discussed.