  I discuss threshold resummation at NNLL accuracy in the standard moment-space
approach in perturbative QCD for top-pair and single-top production. For top
quark pair production I present new approximate NNLO results for the total
cross section and for the top quark transverse momentum and rapidity
distributions at 8 TeV LHC energy. I discuss the accuracy of the soft-gluon
approximation and show that the NLO and NNLO approximate results from
resummation are practically indistinguishable from exact NLO and partial NNLO
results. For single top production I present new approximate NNLO results for
the total cross sections in all three channels at the LHC and also for the top
quark transverse momentum distributions in t-channel production and in
top-quark associated production with a W boson. For both ttbar and single-top
production the agreement of theoretical results with LHC and Tevatron data is
excellent.
