  In the standard hot big bang nucleosynthesis (BBN) model the primordial
abundances of H, H2, He3, He4, and Li7, fix the baryon density of the universe,
$\Omega_b$, via the baryon-to-photon ratio, $\eta$, for a given Hubble
parameter. Recent observations of Li show that its intrinsic dispersion in
metal-poor stars is essentially zero, and the random error in the mean Li
abundance is negligible. However, a decreasing trend in the Li abundance
towards lower metallicity, plus Li6 detections, indicate that its primordial
abundance can be inferred only after allowing for nucleosynthesis processes in
the Galaxy (Galactic chemical evolution (GCE)). We show that the Li vs Fe trend
provides a tough discriminant between alternative models for GCE of
light-elements. We critically assess current systematic uncertainties, and
determine the primordial Li abundance within new, much tighter limits. We show
that the Li constraint on $\Omega_b$ is now limited principally by
uncertainties in the nuclear cross-sections used in BBN {\it calculations}, not
by the abundance itself. A clearer understanding of systematics allows for a
much more accurate inference of the primordial Li abundance, sharpening the
comparison with He4 and deuterium and the resulting test of BBN. We find that
the Li data are in good agreement with He4 and with ``high'' deuterium values,
but that low deuterium abundances are at best marginally within the Li range.
