Future radio telescopes will open a new era in the observation of weak, extended magnetic fields in nearby galaxies. Observing low-frequency synchrotron emission with LOFAR will allow us to trace low-energy cosmic-ray electrons which suffer less from energy losses and can propagate far away from their origin. Deep observations of diffuse polarized emission and of RM grids towards polarized background sources with the SKA and its pathfinders will reveal the structure of weak magnetic fields in the outer regions and halos of galaxies and the transition to intergalactic space.