Deuterium, Big-Bang Nucleosynthesis and the Baryon Density Abstract: The amount of deuterium produced in the first few minutes of the hot big bang is a sensitive probe of entropy per baryon during the early universe. High resolution spectroscopic measurements of the deuterium abundance in high redshift, nearly pristine abosrption systems place strong constraints on the primordial deuterium ratio, D/H = 2.8x10^-5 (15% uncertainty) and the cosmological baryon density Omega_b h^2 = 0.021 +- 0.001 I will highlight the main difficulties and possible systematic uncertainties in the deuterium measurements, and will compare the results with the recent constraints from anisotropy measurements of the cosmic microwave background.