We report new calculations of reactor antineutrino spectra including the latest information from nuclear databases and a detailed error budget. The first part of this work is the so-called ab initio approach where the total antineutrino spectrum is built from the sum of all beta-branches of all fission products predicted by an evolution code. Systematic effects and missing information in nuclear databases lead to final relative uncertainties in the 10 to 20% range. A prediction of the antineutrino spectrum associated with the fission of 238U is given based on this ab initio method. For the dominant isotopes 235U and 239Pu, we developed a more accurate approach combining information from nuclear databases and reference electron spectra associated with the fission of 235U, 239Pu and 241Pu, measured at ILL in the 80's. We show how the anchor point of the measured total beta-spectra can be used to suppress the uncertainty in nuclear databases while taking advantage of all the information they contain. We provide new reference antineutrino spectra for 235U, 239Pu and 241Pu isotopes in the 2-8 MeV range. While the shapes of the spectra and their uncertainties are comparable to that of the previous analysis of the ILL data, the normalization is shifted by about +3% on average. In the perspective of the re-analysis of past experiments and direct use of these results by upcoming oscillation experiments, we discuss the various sources of errors and their correlations as well as the corrections induced by off equilibrium effects.