The QED radiative corrections to virtual Compton scattering (reaction ep-->
ep gamma) are calculated to first order in alpha(em)=e(2)/4 pi. A detailed
study is presented for the one-loop virtual corrections and for the first o
rder soft-photon emission contributions. Furthermore, a full numerical calc
ulation is given for the radiative tail, corresponding to photon emission p
rocesses, where the photon energy is not very small compared with the lepto
n momenta. We compare our results with existing works on elastic electron-p
roton scattering, and show for the ep-->ep gamma reaction how the observabl
es are modified due to these first order QED radiative corrections. We show
results for both unpolarized and polarized observables of virtual Compton
scattering in the low energy region (where one is sensitive to the generali
zed polarizabilities of the nucleon), as well as for the deeply virtual Com
pton scattering.