Résumé
The epoch of Big Bang nucleosynthesis presents a precision observational test of cosmic conditions at cosmic temperatures below a few MeV. Comparison of theoretically predicted abundances of $^2$H, $^3$He, $^4$He, and $^7$Li with observationally inferred primordial abundances has led to the standard model of Big Bang nucleosythesis (SBBN). In this talk I review the observational determination of light-element abundances, with particular focus on $^7$Li and $^2$H. It is found that predicted $^7$Li production in SBBN is around a factor three higher than the observationally inferred abundance of this isotope. Astrophysical effects, as well as nuclear reaction rate uncertainties, which may or may not explain such a discrepancy are reviewed. Recent observations of $^6$Li abundances in low-metallicity halo stars have revealed a surprisingly high $^6$Li abundance in disaccord with expectations of $^6$Li production by galactic cosmic rays. I review the proposed astrophysical scenarios which may reproduce the data. In the second part of this talk, it is assumed that the $^6$Li and $^7$Li anomalies are signs of physics beyond the standard model of particle physics and BBN. The currently proposed modifications to BBN to account for these anomalies are reviewed. Particularly promising may be the possible existence of supersymmetry with the superpartner of the graviton, the gravitino, being the dark matter. In this case, the decay of either the superpartner of the U(1) hypercharge gauge boson, or the superpartner of the tau-lepton may decay during BBN, thereby solving both problems at once. The resulting cosmology, implications for the LHC, and the physics entering the BBN calculations are highlighted.