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’.