  I present a calculation of next-to-next-to-next-to-leading-order (NNNLO)
soft-gluon corrections for differential distributions in top-antitop pair
production in hadronic collisions. Approximate NNNLO (aNNNLO) results are
obtained from soft-gluon resummation. Theoretical predictions are shown for the
top-quark aNNNLO transverse momentum ($p_T$) and rapidity distributions at LHC
and Tevatron energies. The aNNNLO corrections enhance previous results for the
distributions but have smaller theoretical uncertainties.
