  The origin of magnetic fields in the Universe is an open problem in
astrophysics and fundamental physics. Our present-day knowledge is limited to
regions of strong magnetic fields and to star-forming disks of galaxies.
Low-energy electrons emitting at low frequencies suffer less from energy losses
and can propagate further into the intergalactic medium. The prospects are
threefold: Firstly, LOFAR will map the structure of weak magnetic fields in the
outer regions and halos of galaxies and in the Milky Way. Polarized emission is
an excellent tracer of past interactions with other galaxies and with the
interstellar medium. Secondly, high-resolution polarization observations are
needed at high frequencies with the EVLA and SKA to trace the structure of
magnetic fields in the disks and central regions of galaxies in unprecedented
detail. The SKA can also detect polarized emission from distant, unresolved
galaxies. Thirdly, Faraday rotation measures (RM) are signatures of regular
magnetic fields generated by the dynamo mechanism. All-sky surveys of Faraday
rotation measures (RM) towards polarized background sources will be used to
model the structure and strength of the regular magnetic fields in the Milky
Way, the interstellar medium of galaxies and the intergalactic medium. This
will open a new era in the observation of cosmic magnetic fields. "Key Science"
Projects on cosmic magnetism are organized for the Low Frequency Array (LOFAR),
the planned Square Kilometre Array (SKA) and the Australian SKA Pathfinder
telescope (ASKAP).
