  The numerical unitarity approach has been important for obtaining reliable
QCD predictions for the LHC. Here I discuss the extension of the approach
beyond the leading quantum corrections for computing multi-loop amplitudes. The
numerical unitarity approach requires a suitable parametrisation of the loop
integrands as a sum of terms that integrate to zero (surface terms) and master
integrands. The construction and classification of suitable surface terms which
match the propagators structures of Feynman amplitudes is the main technical
advance discussed. A number of spin-offs for integral reduction and further
formal questions are briefly reviewed.
