  I discuss and compare several approaches to higher-order calculations of top
quark production. I study the relative effectiveness of the approaches in
approximating the exact NNLO results for the top-pair total cross section and
highlight the theoretical and numerical differences between them. I show that
the results from my soft-gluon resummation method are nearly identical to the
exact NNLO cross section at all LHC and Tevatron energies. This agreement has
important consequences for the validity of existing approximate NNLO
differential distributions, for further refinements of the predictions, and for
applications to other processes such as single-top production. I also compare
approximate NNLO top quark transverse momentum and rapidity distributions with
recent LHC measurements.
