There are a few cross sections that are expected to be measured at the LHC with an experimental error reaching below 10 per cent. One of them is the top-quark pair production cross section. On the theory side, such an accuracy requires the next-to-next-to leading order in the perturbative expansion. In assembling a full prediction, there are different challenges posed by the real radiation and the virtual corrections. We will review the recent progress in the determination of the latter and sketch the theoretical tools to complete the calculation. Some emphasis will also be put on the properties of the cross section in the threshold and the high energy regimes.

Universitat Wurzburg