In this talk we discuss NNLO and N3LO order corrections
to the process gg->HH in the Standard Model. In particular,
we consider three-loop corrections to the form factors entering the virtual
corrections in the large-mt
limit and compute five expansion terms.
In the same approximation we also evaluate the
real radiation corrections at NNLO. Finally, we present
a building block for the N3LO corrections, namely the
four-loop matching coefficient for the effective coupling
of two Higgs bosons to gluons.