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.Comment: 7 pages, 7 figures; presented at EPS-HEP 2013, Stockholm, Sweden,
July 18-24, 201