Soft-gluon resummations and NNNLO expansions

I discuss the effectiveness of soft-gluon resummations in describing higher-order corrections. I present a comparison of recent resummation approaches and their relative successes in approximating complete NNLO corrections. I also discuss fixed-order expansions through NNNLO and present some recent applications to QCD hard-scattering processes, including top-antitop pair production, single-top production, and W production at large transverse momentum.