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.