The origin of magnetic fields in stars, galaxies and clusters is an open problem in astrophysics. The next-generation radio telescopes <i>Low Frequency Array (LOFAR)</i> and <i>Square Kilometre Array (SKA)</i> will revolutionize the study of cosmic magnetism. "The origin and evolution of cosmic magnetism" is a key science project for SKA. The planned all-sky survey of Faraday rotation measures (RM) at 1.4 GHz will be used to model the structure and strength of the magnetic fields in the intergalactic medium, the interstellar medium of intervening galaxies, and in the Milky Way. A complementary survey of selected regions at around 200 MHz is planned as a key project for LOFAR. <i>Spectro-polarimetry</i> applied to the large number of spectral channels available for LOFAR and SKA will allow to separate RM components from distinct foreground and background regions and to perform 3-D <i>Faraday tomography</i> of the interstellar medium of the Milky Way and nearby galaxies. &ndash; Deep polarization mapping with LOFAR and SKA will open a new era also in the observation of synchrotron emission from magnetic fields. LOFAR's sensitivity will allow to map the structure of weak, extended magnetic fields in the halos of galaxies, in galaxy clusters, and possibly in the intergalactic medium. Polarization observations with SKA at higher frequencies (1&ndash;10 GHz) will show the detailed magnetic field structure within the disks and central regions of galaxies, with much higher angular resolution than present-day radio telescopes.