I discuss the motivation for resummation of the effects of initial-state soft
gluon radiation, to all orders in the strong coupling strength, for processes
in which the near-threshold region in the partonic subenergy is important. I
summarize the method of "perturbative resummation" and its application to the
calculation of the total cross section for top quark production at hadron
colliders. Comments are included on the differences between the treatment of
subleading logarithmic terms in this method and in other approaches.Comment: 15 pages. latex, one figure. Invited paper to be published in the
Proceedings of the Symposium on QCD Corrections and New Physics, Hiroshima,
October 27 - 29, 199