  Magnetic fields appear everywhere in the universe. From stars and galaxies,
all the way to galaxy clusters and remote protogalactic clouds magnetic fields
of considerable strength and size have been repeatedly observed. Despite their
widespread presence, however, the origin of cosmic magnetic fields is still a
mystery. The galactic dynamo is believed capable of amplifying weak magnetic
seeds to strengths like those measured in ours and other galaxies, but the
question is where do these seed fields come from? Are they a product of late,
post-recombination, physics or are they truly cosmological in origin? The idea
of primordial magnetism is attractive because it makes the large-scale magnetic
fields, especially those found in early protogalactic systems, easier to
explain. As a result, a host of different scenarios have appeared in the
literature. Nevertheless, early magnetogenesis is not problem free, with a
number of issues remaining open and a matter of debate. We review the question
of primordial magnetic fields and consider the limits set on their strength by
the current observational data. The various mechanisms of pre-recombination
magnetogenesis are presented and their advantages and shortcomings are debated.
We consider both classical and quantum scenarios, that operate within as well
as outside the standard model, and also discuss how future observations could
be used to decide whether the large-scale magnetic fields we see in the
universe today are truly primordial or not.
