  We present the dispersion relation approach based on unitarity and
analyticity to evaluate the two-photon exchange contribution to elastic
electron-proton scattering. The leading elastic and first inelastic $\pi N$
intermediate state contributions are accounted for in the region of small
momentum transfer $Q^2 < 1~\mathrm{GeV}^2$ based on the available data input.
The novel methods of analytical continuation allow us to exploit the MAMI form
factor data and the MAID parameterization for the pion electroproduction
amplitudes as input in the calculation. The results are compared to the recent
CLAS, VEPP-3 and OLYMPUS data as well as to the full two-photon exchange
correction in the near-forward approximation, which is based on the Christy and
Bosted unpolarized structure functions fit. Additionally, predictions are given
for a forthcoming muon-proton scattering experiment.
