High statistics measurements of light-by-light scattering, made accessible using relativistic heavy-ion beams provide a precise and unique opportunity to investigate extensions of the Standard Model, such as the presence of axion-like particles. The corresponding measurement of the ATLAS Collaboration is discussed as well as the study of exclusive dilepton production (electron, muon, and tau pairs) in photon-photon fusion. Furthermore, the tau-pair production measurements are used to constrain the tau lepton's anomalous magnetic dipole moment.