Photon-photon scattering: a tutorial

Long-established results for the low-energy photon-photon scattering, gamma gamma --> gamma gamma, have recently been questioned. We analyze that claim and demonstrate that it is inconsistent with experience. We demonstrate that the mistake originates from an erroneous manipulation of divergent integrals and discuss the connection with another recent claim about the Higgs decay into two photons. We show a simple way of correctly computing the low-energy gamma gamma scattering.