Primordial nucleosynthesis, or big bang nucleosynthesis (BBN), is one of the three evidences for the big bang model, together with the expansion of the universe and the cosmic microwave background. There is a good global agreement over a range of nine orders of magnitude between abundances of 4He, D, 3He and 7Li deduced from observations, and calculated in primordial nucleosynthesis. However, there remains a yet-unexplained discrepancy of a factor 3, between the calculated and observed lithium primordial abundances, that has not been reduced, neither by recent nuclear physics experiments, nor by new observations. The precision in deuterium observations in cosmological clouds has recently improved dramatically, so that nuclear cross-sections involved in deuterium BBN needs to be known with similar precision. We will briefly discuss nuclear aspects related to the BBN of Li and D, BBN with nonstandard neutron sources, and finally, improved sensitivity studies using a Monte Carlo method that can be used in other sites of nucleosynthesis.