  The origin of magnetic fields in the Universe is an open problem in
astrophysics and fundamental physics. "Cosmic Magnetism" has been accepted as
Key Science Project both for the Low Frequency Array (LOFAR, under
construction) and the planned Square Kilometre Array (SKA). At low frequencies
LOFAR and SKA will allow to map the structure of weak magnetic fields in the
outer regions and halos of galaxies, in galaxy clusters and in the Milky Way.
High-resolution polarization observations at high frequencies with the SKA will
trace magnetic fields in the disks and central regions of galaxies in
unprecedented detail. All-sky surveys of Faraday rotation measures (RM) towards
polarized background sources will be used to model the structure and strength
of the magnetic fields in the Milky Way, the interstellar medium of galaxies
and the intergalactic medium. The new method of "RM Synthesis", applied to
spectro-polarimetric data cubes, will separate RM components from different
distances and allow 3-D "Faraday tomography". Magnetic fields in distant
galaxies and clusters and in intergalactic filaments will be searched for by
deep imaging of weak synchrotron emission and of RM towards background sources.
This will open a new era in the observation of cosmic magnetic fields.
