  Using the recently derived NNLO cross sections \cite{Czakon:2013goa}, we
provide NNLO+NNLL theoretical predictions for top quark pair production based
on all the available NNLO PDF sets, and compare them with the most precise LHC
and Tevatron data. In this comparison we study in detail the PDF uncertainty
and the scale, $m_t$ and $\alpha_s$ dependence of the theoretical predictions
for each PDF set. Next, we observe that top quark pair production provides a
powerful direct constraint on the gluon PDF at large $x$, and include Tevatron
and LHC top pair data consistently into a global NNLO PDF fit. We then explore
the phenomenological consequences of the reduced gluon PDF uncertainties, by
showing how they can improve predictions for Beyond the Standard Model
processes at the LHC. Finally, we update to full NNLO+NNLL the theoretical
predictions for the ratio of top quark cross sections between different LHC
center of mass energies, as well as the cross sections for hypothetical heavy
fourth-generation quark production at the LHC.
