Exploring the IR structure of massless gauge theories

The problem of infrared divergences in gauge-theory scattering amplitudes is as old as quantum field theory, and has been 'solved’ many times, with increasing degrees of sophistication. Perhaps surprisingly, it is still at the forefront of current research, both in view of new theoretical developments, and for phenomenological applications. I will provide an overview of the state of the art for infrared factorisation of scattering amplitudes, and then I will briefly present two current research directions: the problem of infrared subtraction for the precision calculation of collider observables, and the surprising connection between infrared behaviour in d=4 and two-dimensional conformal field theories on the `celestial sphere’.