Photon-photon fusion is a rare process at hadron and ion colliders. It is particularly interesting as a remarkably clean interaction with little (if any) remnant activity from the interacting particles. We present the status of photon-photon fusion measurements with the ATLAS detector at the LHC. This includes the production of lepton pairs and photon pairs (via light-by-light scattering) in heavy ion (Pb+Pb) collisions, as well as photon-photon fusion measurements in proton--proton collisions that contain two charged leptons in the final state. The experimental techniques used in the proton-proton and heavy-ion measurements are different, for example due to the different amounts of pile-up activity, and are also discussed.