Recent progress on infrared singularities

Over the past couple of years we have had significant progress in determining long-distance singularities in gauge-theory scattering amplitudes of massless particles beyond the planar limit. Upon considering all kinematic invariants much larger than the QCD scale, the singularities factorise into universal soft and jet functions, leaving behind a finite hard-interaction amplitude. Such factorization can now be implemented in full to three loops for arbitrary scattering processes of massless partons. In particular, the soft anomalous dimension for a general configuration of $n$ coloured particles was computed to this order, where it displays for the first time non-dipole interactions that correlate the colour and kinematic degrees of freedom of three and four particles. In parallel, there has been progress in understanding amplitudes and their singularities in special kinematic limits, such as collinear limits of multi-leg amplitudes and the high-energy limit in $2\to 2$ scattering. These relate respectively to different factorization properties of gauge-theory amplitudes. In this talk I describe the state of the art and illustrate the interplay between the analysis of the singularities for general kinematics and the properties of amplitudes in special kinematic limits.