Status of double virtual NNLO QCD corrections for high multiplicity processes

Pushing the reach of NNLO QCD predictions to $2\to3$ production processes is one of the pillars of precision phenomenology program at the LHC. In this talk we will overview recent results and developments in the calculation of two-loop five-point amplitudes contributing towards achieving this goal. We will discuss challenges encountered in advancing the state-of-the-art beyond the class of massless five-point scattering. We will then present a basis set of transcendental functions sufficient to express any planar two-loop five-particle scattering amplitude with one external massive leg. This basis greatly facilitates derivation of compact analytic form of scattering amplitudes, and opens a possibility of their fast and reliable numerical evaluation. Applications for phenomenology of electroweak boson production can be reasonably anticipated in the near future.