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An important ingredient for the precision program at the LHC are sophisticated higher order perturbative QCD calculations. A key difficulty of these calculations is the appearance of a non-trivial infrared singularity structure, that must be dealt with. In this talk, I will discuss this problem and some of its proposed solutions. In particular, I will describe the nested soft-collinear subtraction scheme, which is the first method which is both fully local and fully analytic. I will give an overview of the construction, emphasising its physical transparency and relative compactness, and will give a short outlook on future developments.