Cosmological Magnetogenesis: what we know and what we would like to know

Problems and perspectives concerning the existence of large-scale magnetic fields are described. Heeding observations, possible origins and implications of magnetic fields in spiral galaxies and in regular clusters are scrutinized in different cosmological frameworks including scenarios where conformal invariance is broken because of the evolution of the gauge couplings.The generation of the BAU via hypermagnetic knots is reviewed. It is also argued that stochastic GW backgrounds can be generated in the LISA frequency range thanks to the presence of hypermagnetic fields.