We review the recent advances in the calculation of two-loop QCD corrections for massless five-point scattering that paved the way for their broad phenomenological applications in calculation of NNLO QCD predictions. We first discuss the construction of a transcendental function basis which facilitates derivation of compact analytic representations for two-loop amplitudes and enables their fast and stable numerical evaluation over physical phase space. We then present the recent calculations of

more »

... the leading-color two-loop corrections for hadroproduction of three photons and three jets.