  We review recent progress in determining the infrared singularity structure
of on-shell scattering amplitudes in massless gauge theories. We present a
simple ansatz where soft singularities of any scattering amplitude of massless
partons, to any loop order, are written as a sum over colour dipoles, governed
by the cusp anomalous dimension. We explain how this formula was obtained, as
the simplest solution to a newly-derived set of equations constraining the
singularity structure to all orders. We emphasize the physical ideas underlying
this derivation: the factorization of soft and collinear modes, the special
properties of soft gluon interactions, and the notion of the cusp anomaly.
Finally, we briefly discuss potential multi-loop contributions going beyond the
sum-over-dipoles formula, which cannot be excluded at present.
