Two-photon exchange in elastic electron-proton scattering

We review recent theoretical and experimental progress on the role of two-photon exchange (TPE) in electron-proton scattering at low to moderate momentum transfers. We make a detailed comparison and analysis of the results of competing experiments on the ratio of e+p to e−p elastic scattering cross sections, and of the theoretical calculations describing them. A summary of the current experimental situation is provided, along with an outlook for future experiments.