Higgs boson pair production is the most promising process for testing the scalar potential
of the SM beyond the quadratic term. The next-to-leading order QCD corrections for this gluon-fusion
process are large and the dependence on the renormalization scheme of the top quark mass are sizeable.
In this seminar I will discuss the current state of theoretical predictions for the total cross-section and
present recent progress on the calculation of NNLO real radiation corrections beyond the infinitely
heavy top quark approximation.