Physics with Penning traps towards the precision limit

An overview is given on recent measurements with extreme precision on single or few cooled ions stored in Penning traps. On the one hand, mass measurements provide crucial information for atomic physics as well as for testing fundamental symmetries. On the other hand, g-factor measurements of the bound electron in highly-charged hydrogen-like ions allow for the determination of fundamental constants and for constraining Quantum Electrodynamics. For example, the most stringent test of CPT symmetry in the baryonic sector could be performed by mass comparison of the antiproton with H^- and the knowledge of the electron atomic mass could be improved by more than an order of magnitude.