  We review the possible mechanisms for the generation of cosmological magnetic
fields, discuss their evolution in an expanding Universe filled with the cosmic
plasma and provide a critical review of the literature on the subject. We put
special emphasis on the prospects for observational tests of the proposed
cosmological magnetogenesis scenarios using radio and gamma-ray astronomy and
ultra high energy cosmic rays. We argue that primordial magnetic fields are
observationally testable. They lead to magnetic fields in the intergalactic
medium with magnetic field strength and correlation length in a well defined
range. We also state the unsolved questions in this fascinating open problem of
cosmology and propose future observations to address them.
