  We review the role of two-photon exchange (TPE) in electron-hadron
scattering, focusing in particular on hadronic frameworks suitable for
describing the low and moderate Q^2 region relevant to most experimental
studies. We discuss the effects of TPE on the extraction of nucleon form
factors and their role in the resolution of the proton electric to magnetic
form factor ratio puzzle. The implications of TPE on various other observables,
including neutron form factors, electroproduction of resonances and pions, and
nuclear form factors, are summarized. Measurements seeking to directly identify
TPE effects, such as through the angular dependence of polarization
measurements, nonlinear epsilon contributions to the cross sections, and via e+
p to e- p cross section ratios, are also outlined. In the weak sector, we
describe the role of TPE and gamma-Z interference in parity-violating electron
scattering, and assess their impact on the extraction of the strange form
factors of the nucleon and the weak charge of the proton.
