  We discuss how colour flows can be used to simplify the computation of matrix
elements, and in the context of parton shower Monte Carlos with accuracy beyond
leading-colour. We show that, by systematically employing them, the results for
tree-level matrix elements and their soft limits can be given in a closed form
that does not require any colour algebra. The colour flows that we define are a
natural generalization of those exploited by existing Monte Carlos; we
construct their representations in terms of different but conceptually
equivalent quantities, namely colour loops and dipole graphs, and examine how
these objects may help to extend the accuracy of Monte Carlos through the
inclusion of subleading-colour effects. We show how the results that we obtain
can be used, with trivial modifications, in the context of QCD+QED simulations,
since we are able to put the gluon and photon soft-radiation patterns on the
same footing. We also comment on some peculiar properties of gluon-only colour
flows, and their relationships with established results in the mathematics of
permutations.
