From the observations of the anisotropies of the Cosmic Microwave Background (CMB) radiation, the WMAP satellite has provided a determination of the baryonic density of the Universe, &OHgr;bh2, with an unprecedented precision. This imposes a careful reanalysis of the standard Big‐Bang Nucleosynthesis (SBBN) calculations. We have updated our previous calculations using thermonuclear reaction rates provided by a new analysis of experimental nuclear data constrained byR‐matrix theory. Combining these BBN results with the &OHgr;bh2value from WMAP, we deduce the light element (4He,D,3Heand7Li) primordial abundances and compare them with spectroscopic observations. There is a very good agreement with deuterium observed in cosmological clouds, which strengthens the confidence on the estimated baryonic density of the Universe. However, there is an important discrepancy between the deduced7Liabundance and the one observed in halo stars of our Galaxy, supposed, until now, to represent the primordial abundance of this isotope. The origin of this discrepancy, observational, nuclear or more fundamental remains to be clarified. The possible role of the up to now neglected7Be(d,p)2&agr; and7Be(d,&agr;)5Li reactions is considered. © 2004 American Institute of Physics