  We discuss cross sections for $tW$ production in proton-proton collisions at
the LHC and at higher-energy colliders with energies of up to 100 TeV. We find
that, remarkably, the soft-gluon corrections are numerically dominant even at
very high collider energies. We present results with soft-gluon corrections at
approximate NNLO and approximate N$^3$LO matched to complete NLO results. These
higher-order corrections are large and need to be included for better
theoretical accuracy and smaller scale dependence. Total cross sections as well
as top-quark and $W$-boson transverse-momentum and rapidity distributions are
presented using various recent sets of parton distribution functions.
