QCD higher-order corrections current status and prospects

Data collected at the LHC and the future collider FCC require precise theoretical predictions for revealing the nature of elementary particle interactions and possible signatures of new physics beyond the Standard Model. The precision of our theoretical predictions is related to our ability to compute scattering amplitudes at higher orders in perturbation theory. I will review the scattering amplitudes computation starting with the leading-order (LO) and the next-to-leading-order (NLO) approximations. The recent progress at the two-loop frontier will be discussed along with next-to-next-to-leading-order (NNLO) results for 2→ 3 processes.