Observations show that galaxies have magnetic fields with a component that is coherent over a large fraction of the galaxy, with defined field strength and coherence scale. Understanding the origin of these fields is one of the more challenging questions of modern astrophysics. There are currently two pictures: a bottom-up (astrophysical) one, generating the seed field on smaller scales, and a top-down (cosmological) version, generating the seed field prior to galaxy formation on scales that are now large. In my talk I will discuss briefly several relevant questions: (i) How and when was the magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Can the amplitude and statistical properties of this seed magnetic field explain the properties of the observed magnetic fields in large-scale structures? (iv) Is the seed magnetic field detectable through cosmological observations? And if so, (v) what are the observational constraints on such a primordial magnetic field?