  We assess the status of big-bang nucleosynthesis (BBN) in light of the final
Planck data release and other recent developments, and in anticipation of
future measurements. Planck data fix the cosmic baryon density to 0.9%
precision, and determine the helium abundance and effective number of neutrinos
with precision approaching that of astronomical and BBN determinations
respectively. In addition, new high-redshift measurements give D/H to better
precision than theoretical predictions, and new Li/H data reconfirm the lithium
problem. We present new ${}^{7}{\rm Be}(n,p){}^{7}{\rm Li}$ rates using new
neutron capture measurements; we have also examined the effect of proposed
changes in the $d(p,\gamma){}^{3}{\rm He}$ rates. Using these results we
perform a series of likelihood analyses. We assess BBN/CMB consistency, with
attention to how our results depend on the choice of Planck data, as well as
how the results depend on the choice of non-BBN, non-Planck data sets. Most
importantly the lithium problem remains, and indeed is more acute given the
very tight D/H observational constraints; new neutron capture data reveals
systematics that somewhat increases uncertainty and thus slightly reduces but
does not essentially change the problem. We confirm that $d(p,\gamma){}^{3}{\rm
He}$ theoretical rates brings D/H out of agreement and slightly increases 7Li;
new experimental data are needed at BBN energies. Setting the lithium problem
aside, we find the effective number of neutrino species at BBN is $N_\nu = 2.86
\pm 0.15$. Future CMB Stage-4 measurements promise substantial improvements in
BBN parameters: helium abundance determinations will be competitive with the
best astronomical determinations, and $N_{\rm eff}$ will approach sensitivities
capable of detecting the effects of Standard Model neutrino heating of the
primordial plasma. (Abridged)
