Sudakov resummations at higher orders

We summarize our recent results on the resummation of hard-scattering coefficient functions and on-shell form factors in massless perturbative QCD. The threshold resummation has been extended to the fourth logarithmic order for deep-inelastic scattering, Drell-Yan lepton pair production and Higgs production via gluon-gluon fusion. The leading six infrared pole terms have been derived to all orders in the strong coupling constant for the photon-quark-quark and the (heavy-top) Higgs-gluon-gluon form factors. These results have many implications, most notably they lead to a new best estimate for the Higgs production cross section at the LHC.