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Cross-sections in perturbative QCD are plagued by large corrections from soft and collinear radiation. The most singular terms are known to be universal, which allows their resummation to all orders in the coupling, which cures the perturbative expansion of the cross-section. In this talk, I will give an introduction on how these large corrections arise, how resummation solves the issue, and whether we can expect the same universal structure for a class of next-to-singular contributions.