Precision big bang nucleosynthesis and the status of deuterium

Primordial nucleosynthesis or Big-Bang Nucleosynthesis (BBN) happens during the first 300 seconds of our Universe. It is one of the three evidences for the big-bang model, together with the cosmological expansion and the Cosmic Microwave Background (CMB). Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, it has become a parameter free model. Since the most recent measurements of primordial deuterium and Helium-4 abundances reach the percent level in precision, it is necessary to obtain a similar precision in theoretical predictions. I will review the basic physics of primordial cosmology and BBN and then review the various effects which need to be taken into account at that epoch in order to obtain such precision. I will also discuss a tension in primordial deuterium which has emerged following a recent update on one of the key nuclear rates.