  This review concerns the origin and the possible effects of magnetic fields
in the early Universe. We start by providing to the reader with a short
overview of the current state of art of observations of cosmic magnetic fields.
We then illustrate the arguments in favour of a primordial origin of magnetic
fields in the galaxies and in the clusters of galaxies. We argue that the most
promising way to test this hypothesis is to look for possible imprints of
magnetic fields on the temperature and polarization anisotropies of the cosmic
microwave background radiation (CMBR). With this purpose in mind, we provide a
review of the most relevant effects of magnetic fields on the CMBR. A long
chapter of this review is dedicated to particle physics inspired models which
predict the generation of magnetic fields during the early Universe evolution.
Although it is still unclear if any of these models can really explain the
origin of galactic and intergalactic magnetic fields, we show that interesting
effects may arise anyhow. Among these effects, we discuss the consequences of
strong magnetic fields on the big-bang nucleosynthesis, on the masses and
couplings of the matter constituents, on the electroweak phase transition, and
on the baryon and lepton number violating sphaleron processes. Several
intriguing common aspects, and possible interplay, of magnetogenesis and
baryogenesis are also dicussed.
