  I review the recent progress in studying long-distance singularities in
gauge-theory scattering amplitudes in terms of Wilson lines. The non-Abelian
exponentiation theorem, which has been recently generalised to the case of
multi-leg amplitudes, states that diagrams exponentiate such that the colour
factors in the exponent are fully connected. After a brief review of the
diagrammatic approach to soft gluon exponentiation, I sketch the method we used
to prove the theorem and illustrate how connected colour factors emerge in the
exponent in webs that are formed by sets of multiple-gluon-exchange diagrams.
In the second part of the talk I report on recent progress in evaluating the
corresponding integrals, where a major simplification is achieved upon
formulating the calculation in terms of subtracted webs. I argue that the
contributions of all multiple-gluon-exchange diagrams to the soft anomalous
dimension take the form of products of specific polylogarithmic functions, each
depending on a single cusp angle.
