  We extract the two-photon exchange (TPE) contributions to electron--proton
elastic scattering using two parametrizations and compare the results to
different phenomenological extractions and direct calculations of the TPE
effects. We find that many of the extractions give similar results, and
highlight the common assumptions and the impact of not including such
assumptions. We provide a simple parametrization of the TPE contribution to the
unpolarized cross section, along with an estimate of the fit uncertainties and
the uncertainties associated with the assumptions made in the extraction. We
look at the contributions as extracted from various e--p elastic scattering
observables, and make predictions for ratio $R^{e^{+} e^{-}}$ of
positron-proton to electron-proton elastic scattering cross sections.
