  The origin of cosmic magnetism is an issue of fundamental importance in
astrophysics. We review here some of the ideas of how large scale magnetic
fields in the universe, particularly in galaxies and galaxy clusters could
arise. The popular paradigm involves the generation of a seed magnetic field
followed by turbulent dynamo amplification of the seed field. We first outline
various seed field generation mechanisms including Biermann batteries. These in
general give a field much smaller than the observed field and so they require
further amplification by dynamo action. The basic idea behind fluctuation
dynamos, as applied to cluster magnetism and the mean-field helical dynamo as
applied to disk galaxies, are outlined. Major difficulties with the dynamo
paradigm are considered. It is particularly important to understand the
nonlinear saturation of dynamos, and whether the fields produced are coherent
enough on large-scales to explain the observed fields in galaxies and clusters.
At the same time the alternative possibility of a primordial field lacks firm
theoretical support but can have very interesting observational consequences.
