Newνe, e scattering experiments aimed for sensitive searches of the νe magnetic moment and projects to explore small mixing angle oscillations at reactors call for a better understanding of the reactor antineutrino spectrum. Here we consider six components, which contribute to the total νe spectrum generated in nuclear reactor. They are: beta decay of the fission fragments of 235 U, 239 Pu, 238 U and 241 Pu, decay of beta-emitters produced as a result of neutron capture in 238 U and also due to neutron capture in accumulated fission fragments which perturbs the spectrum. For antineutrino energies less than 3.5 MeV we tabulate evolution ofνe spectra corresponding to each of the four fissile isotopes vs fuel irradiation time and their decay after the irradiation is stopped and also estimate relevant uncertainties. Small corrections to the ILL spectra are considered.1 Here F N ≈ 5.5ν e /fission represents summed contribution from beta decays of fission fragments of four fissile isotopes 235 U, 239 Pu, 238 U and 241 Pu, undistorted by their interaction with reactor neutrons, U N ≈ 1.2ν e /fission comes from beta decay of 239 U ⇒ 239 Np ⇒ 239 Pu chain produced via neutron radiative capture in 238 U and δ F N < 0.03ν e /fission originate from neutron capture in accumulated fission fragments and give small but not negligible local distortions of the total energy spectrum of the reactorν e .Plan of this report is as follows: First, we present a short (and incomplete) overview of a half a century long history, which has led to the present understanding of the reactor antineutrinos.Second, we give new results on the computed evolution ofν e energy spectra corresponding to four fissile isotopes vs fuel irradiation time and their decay after the end of the irradiation; we compare all available data and estimate relevant uncertainties.After these data are presented on antineutrinos due to neutron radiative capture in 238 U and in accumulated fission fragments.Finally we consider small corrections to the ILL spectra.