Evidence for scattering of light by light has been found recently in heavy ion collisions by the ATLAS collaboration at the LHC. These collisions produce strong magnetic fields that can influence the probability of light-light scattering events. Motivated by these findings we investigate low energy light-light scattering in the presence of spatially homogeneous magnetic background fields in the Euler-Heisenberg theory. We derive the scattering matrix element for four external photons in Euler-Heisenberg theory. With this we compute the full analytical differential cross section in the limit of weak fields and numerically for arbitrary field strengths. For spinor QED we find that scattering parallel to the magnetic field is suppressed. For scattering processes in which none of the involved photons is parallel to the magnetic field we find that the differential cross section for unpolarized photons averaged over final polarizations grows quadratically with the field strength were maximum growth can be found if the scattering plane is perpendicular to the field strength. For scalar QED we find no quadratic growth and the cross section drops quartic in the magnetic field. We conclude that the quadratic growth in the spinor case has its cause in the interaction of spin and magnetic field and show this claim in the worldline formulation of the one loop QED action. For charged vector particles we find a divergence of the cross section at B/B c = 1 which we identify as a consequence of a phase transition to a superconducting vacuum state. |