Soft-gluon Corrections to Hard-scattering Cross Sections Through NNNLO

I present a systematic approach to calculating soft-gluon corrections through next-to-next-to-nextto-leading order for arbitrary hard-scattering cross sections. Using a unified approach, master formulas are derived for processes with both simple and complex color flows. Applications and numerical results are given for some processes of interest, including charged Higgs production and top quark production in the Standard Model and beyond