Three-loop four-particle QCD amplitudes

We present recent advancements in the computation of three-loop four-particle helicity amplitudes in full-color massless QCD. In this contribution, we focus on the $gg\to \gamma \gamma$ process. We show how to obtain compact analytic formulae for the three-loop scattering amplitude. Our results can be expressed in terms of harmonic polylogarithms, which allows for an efficient numerical evaluation. The results presented here can be used for improving theoretical predictions relevant for Higgs physics at hadron colliders.