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In recent years, there has been a revival of Large-N methods in gauge theories, with N being the number of gauged fermion fields. I will present the diagram resummation approach for calculating leading-order Large-N contributions to renormalisation group functions in the appropriate 't Hooft coupling. The technique is applied to a general model based on semi-simple gauge groups featuring Yukawa and quartic couplings. These results can be applied to high-energy regime of most BSM theories featuring a large number of extra matter states. I will conclude by discussing various extensions, in particular applications of the Large-N expansions to finite parts of diagrams, relevant to physical observables such as decay rates.