Could magnetic fields be a relic from the early Universe, arising perhaps during the inflationary epoch when density fluctuations are also generated? Indeed, tentative indications that femto Gauss level magnetic fields pervade even the voids regions almost empty of galaxies favor such an idea. We discuss the prospects for such inflationary magnetogenesis, focusing also on the challenges these theories face. Subsequent evolution depends on our understanding of magnetohydrodynamics in the early universe including the decay laws of magnetically dominated turbulence. Finally, the prospects of detecting primordial fields due to their signals in the Cosmic Microwave Background, structure formation
or stochastic gravitational wave background are discussed.