Overview of recent theoretical work on two-photon exchange

In this contribution I give an overview of recent progress in theoretical calculations of two-photon exchange (TPE) effects in elastic electron-proton scattering. TPE effects are relevant for extractions of proton form factors at high Q2, and of the proton radius at very low Q2. Recent experiments to directly measure hard TPE effects by comparing positron and electron scattering are discussed from a theoretical perspective.