  Magnetic fields are a fundamental part of many astrophysical phenomena, but
the evolution, structure and origin of magnetic fields are still unresolved
problems in physics and astrophysics. When and how were the first fields
generated? Are present-day magnetic fields the result of standard dynamo
action, or do they represent rapid or recent field amplification through other
processes? What role do magnetic fields play in turbulence, cosmic ray
acceleration and structure formation? I explain how the Square Kilometre Array
(SKA), a next-generation radio telescope, can deliver stunning new data-sets
that will address these currently unanswered issues. The foundation for these
experiments will be an all-sky survey of rotation measures, in which Faraday
rotation toward >10^7 background sources will provide a dense grid for probing
magnetism in the Milky Way, nearby galaxies, and in distant galaxies, clusters
and protogalaxies. Using these data, we can map out the evolution of magnetized
structures from redshifts z > 3 to the present, can distinguish between
different origins for seed magnetic fields in galaxies, and can develop a
detailed model of the magnetic field geometry of the intergalactic medium and
of the overall Universe. In addition, the SKA will certainly discover new
magnetic phenomena beyond what we can currently predict or imagine.
