  Big-bang nucleosynthesis (BBN) describes the production of the lightest
nuclides via a dynamic interplay among the four fundamental forces during the
first seconds of cosmic time. We briefly overview the essentials of this
physics, and present new calculations of light element abundances through li6
and li7, with updated nuclear reactions and uncertainties including those in
the neutron lifetime. We provide fits to these results as a function of baryon
density and of the number of neutrino flavors, N_nu. We review recent
developments in BBN, particularly new, precision Planck cosmic microwave
background (CMB) measurements that now probe the baryon density, helium
content, and the effective number of degrees of freedom, n_eff. These
measurements allow for a tight test of BBN and of cosmology using CMB data
alone. Our likelihood analysis convolves the 2015 Planck data chains with our
BBN output and observational data. Adding astronomical measurements of light
elements strengthens the power of BBN. We include a new determination of the
primordial helium abundance in our likelihood analysis. New D/H observations
are now more precise than the corresponding theoretical predictions, and are
consistent with the Standard Model and the Planck baryon density. Moreover, D/H
now provides a tight measurement of N_nu when combined with the CMB baryon
density, and provides a 2sigma upper limit N_nu < 3.2. The new precision of the
CMB and of D/H observations together leave D/H predictions as the largest
source of uncertainties. Future improvement in BBN calculations will therefore
rely on improved nuclear cross section data. In contrast with D/H and he4, li7
predictions continue to disagree with observations, perhaps pointing to new
physics.
