  A variety of observations suggest that magnetic fields are present in all
galaxies and galaxy clusters. These fields are characterized by a modest
strength (10^{-7}-10^{-5} G) and huge spatial scale (~Mpc). It is generally
assumed that magnetic fields in spiral galaxies arise from the combined action
of differential rotation and helical turbulence, a process known as the
alpha-omega dynamo. However fundamental questions concerning the nature of the
dynamo as well as the origin of the seed fields necessary to prime it remain
unclear. Moreover, the standard alpha-omega dynamo does not explain the
existence of magnetic fields in elliptical galaxies and clusters. The author
summarizes what is known observationally about magnetic fields in galaxies,
clusters, superclusters, and beyond. He then reviews the standard dynamo
paradigm, the challenges that have been leveled against it, and several
alternative scenarios. He concludes with a discussion of astrophysical and
early Universe candidates for seed fields.
