In this thesis, we consider soft-gluon evolution at the amplitude level. We present a general evolution algorithm, which was used originally in the derivation of super-leading logarithms. It includes Coulomb exchanges and applies to generic hard-scattering processes involving any number of coloured partons, resumming soft gluon effects to all orders. To exemplify this algorithm, we perform a calculation of the hemisphere jet mass non-global logarithmic contributions, and show how the algorithm reproduces the well-known Banfi- Marchesini-Smye (BMS) equation. In addition, we explore the colour structures encountered when solving the evolution equations, using the colour flow basis; in preparation of a Monte Carlo implementation. Handling large colour matrices presents a significant challenge to numerical implementations, and we present a means to expand systematically about the leading colour approximation. We subsequently discuss the formulation of our amplitude evolu- tion as a parton branching algorithm, and its implementation into a Monte Carlo code, CVolver. The general-purpose colour machinery underpinning the CVolver framework is reviewed, and we discuss colour-space sampling strate- gies. We build on this framework to simulate high-energy particle collisions, based upon simulated two-jet events, with a restriction on the amount of radiation lying in some region outside of the jets. We present the corresponding cross section results broken down by their colour suppressed terms, alongside independent cross-checks, which validate our implementation. We find that colour suppressed terms can significantly contribute to this cross-section, and find agreement with the results of other authors.