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Amplitudes in theories with massless particles suffer from infrared divergences. While these divergences cancel in physical cross sections, it is nevertheless interesting to understand their structure, since it can be used to predict logarithmically enhanced terms in perturbative computations. In my talk I will explain that the infrared divergences are governed by an anomalous-dimension matrix, which is severely constrained by soft-collinear factorization, non-abelian exponentiation, and the behaviour of amplitudes in collinear limits. I will then present the form of the anomalous-dimension matrix at the four-loop level, which we obtained recently.