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Two-photon exchange contributions to elastic electron scattering are reviewed. The apparent discrepancy between unpolarized Rosenbluth and polarization transfer experiments in the extraction of elastic nucleon form factors is discussed, as well as the understanding of this puzzle in terms of two-photon exchange corrections. Calculations of such corrections within both partonic and hadronic frameworks are reviewed. In view of recent spin-dependent electron scattering data, the relation of the two-photon exchange process to the hyperfine splitting in hydrogen is critically examined. The imaginary part of the two-photon exchange amplitude as can be accessed from the beam-normal spin asymmetry in elastic electron-nucleon scattering is reviewed. Further extensions and open issues in this field are outlined.
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