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 order soft-photon emission contributions. Furthermore, a full numerical calculation is given for the radiative tail, corresponding to 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 ep-->ep 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 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.