I review calculations of soft-gluon corrections for top-quark production in hadron collisions. I describe theoretical formalisms for their resummation and for finite-order expansions. I show that soft-gluon corrections are dominant for a large number of top-quark processes. I discuss top-antitop pair production as well as single-top production, including total cross sections and differential distributions, and compare with data from the LHC and the Tevatron. I also discuss top-quark production in association with charged Higgs bosons, Z bosons, and other particles in models of new physics.