  The QED radiative corrections to virtual Compton scattering (reaction $e p
\to e p \gamma$) are calculated to first order in $\alpha_{em} \equiv e^2 / 4
\pi$. A detailed study is presented for the one-loop virtual corrections and
for the first order soft-photon emission contributions. Furthermore, a full
numerical calculation is given for the radiative tail, corresponding with
photon emission processes, where the photon energy is not very small compared
with the lepton momenta. We compare our results with existing works on elastic
electron-proton scattering, and show for the $e p \to e p \gamma$ reaction how
the observables are modified due to these first order QED radiative
corrections. We show results for both unpolarized and polarized observables of
the virtual Compton scattering in the low energy region (where one is sensitive
to the generalized polarizabilities of the nucleon), as well as for the deeply
virtual Compton scattering.
