  We compute the total top-quark pair production cross section at the Tevatron
and LHC based on approximate NNLO results, and on the summation of threshold
logarithms and Coulomb enhancements to all orders with next-to-next-to-leading
logarithmic (NNLL) accuracy, including bound-state effects. We find
\sigma_{t\bar t} = 7.22^{+0.31+0.71}_{-0.47-0.55} pb at Tevatron and
\sigma_{t\bar t} = 162.6^{+7.4+15.4}_{-7.6-14.7} pb at LHC with 7 TeV c.o.m.
energy, for m_t=173.3 GeV. The implementation of joint soft and Coulomb
resummation, its ambiguities, and the present theoretical uncertainty are
discussed in detail. We further obtain new approximate results at N3LO.
