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.