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Precision predictions for Higgs production at the LHC require fully-differential calculations at NNLO in QCD, which involve the non-trivial cancellation of infrared singularities between real and virtual contributions. In this talk, I will present history, a new computational framework that implements the Nested Soft-Collinear subtraction scheme for arbitrary colour-singlet production processes. After briefly reviewing the current status of infrared subtraction techniques for NNLO calculations, I will introduce the Nested Soft-Collinear scheme and discuss its main features. I will then illustrate our implementation with examples from fully-differential Higgs production at NNLO.