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Over the last 5 years there was tremendous progress in performing computations for hadron colliders at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant. In particular, the computation of fully-inclusive N3LO cross sections for color-singlet production is by now well understood. These results can serve as a template to assess the impact and the importance of N3LO corrections. I will review the state-of-the-art of these computations and what we have learned about hadron collider phenomenology at N3LO