Precise fixed-order multi-jet predictions provide a robust tool to
test our understanding of the phenomenology of hadron colliders at
high energies. Routinely nowadays NLO QCD corrections are included in
the event simulation pipeline of the large experimental LHC
collaborations. In this talk we will review efforts to further improve
predictions for observables related to three-jet production at the LHC
with the inclusion of NNLO QCD corrections. In particular we will
focus on the calculation of correspondent two-loop matrix elements in
the leading-color approximation, which was achieved by using the
recently-developed multi-loop numerical unitarity method and
functional reconstruction techniques.