The two experimental techniques for determining the proton's elastic form factors---unpolarized
cross section measurements and polarization asymmetries---have yielded strikingly discrepant
results. One possible explanation for this discrepancy is that hard two-photon exchange, a radiative
correction that is typically neglected, contributes on the percent level to the elastic
electron-proton cross section. The OLYMPUS experiment tests this hypothesis by measuring the ratio
of positron-proton to electron-proton elastic scattering cross sections. Deviations in this ratio
from unity are a signature of hard two-photon exchange.

The OLYMPUS experiment took place at DESY, in Hamburg, Germany, and over 4 fb$^{-1}$ of integrated
luminosity were acquired by the end of data taking in 2013. 2~GeV electron and positron beams, alternating daily,
were directed through a windowless hydrogen gas target. Scattered leptons and recoiling
protons were detected in coincidence in a toroidal magnetic spectrometer simultaneously over
a wide range of angles. The relative luminosity between electron and positron modes was monitored
redundantly through rates of both forward elastic and symmetric Møller/Bhabha scattering.

The latest results from the OLYMPUS analysis will be presented.