The entire Universe is permeated by magnetic fields. However, little is know about their origin and evolution through all redshifts. In the recent years, magnetohydrodynamic simulations are emerging and provide first views on the magnetic history of the Universe. In this talk, I will presents fully non-ideal MHD simulation of structure formation and show a possible magnetised hierarchical growth scenario. This scenario assumes magnetic field production within the first stars and collapsed objects and later growth and distribution within galaxies. Depending on the invoked transport mechanisms, magnetic fields can be expelled far into the intergalactic medium in a similar fashion as metals.