  Two problems are discussed here. The first one is the 0.4 dex discrepancy
between the 7Li abundance derived from the spectra of metal-poor halo stars on
the one hand, and from Big Bang nucleosynthesis, based on the cosmological
parameters constrained by the WMAP measurements, on the other hand. Lithium,
indeed, can be depleted in the convection zone of unevolved stars. The
understanding of the hydrodynamics of the crucial zone near the bottom of the
convective envelope in dwarfs or turn-off stars of solar metallicity has
recently made enormous progress with the inclusion of internal gravity waves.
However, similar work for metal-poor stars is still lacking. Therefore it is
not yet clear whether the depletion occurring in the metal-poor stars
themselves is adequate to produce a 7Li plateau. The second problem pertains to
the large amount of 6Li recently found in metal-poor halo stars. The
convection-related asymmetry of the 7Li line could mimic the signal attributed
so far to the weak blend of 6Li in the red wing of the 7Li line. Theoretical
computations show that the signal generated by the asymmetry of 7Li is 2.0,
2.1, and 3.7 per cent for [Fe/H]= -3.0, -2.0, -1.0, respectively (Teff =6250 K
and log g=4.0 [cgs]). In addition we re-investigate the statistical properties
of the 6Li plateau and show that previous analyses were biased. Our conclusion
is that the 6Li plateau can be reinterpreted in terms of intrinsic line
asymmetry, without the need to invoke a contribution of 6Li. (abridged)
