Flavour effects play an important role in the statistical evolution of particle number densities in several particle physics phenomena. We present a fully flavour-covariant formalism for transport phenomena, in order to consistently capture all flavour effects in the system. We explicitly study the scenario of Resonant Leptogenesis (RL), and show that flavour covariance requires one to consider generically off-diagonal number densities, rank-4 rate tensors in flavour space, and non-trivial generalization of the discrete symmetries C, P and T. The flavour-covariant transport equations, obtained in our semi-classical framework, describe the effects of three relevant physical phenomena: coherent heavy-neutrino oscillations, quantum decoherence in the charged-lepton sector, and resonant CP violation due to heavy-neutrino mixing. We show quantitatively that the final asymmetry is enhanced by up to an order of magnitude, for electroweak-scale heavy neutrinos, as compared to that obtained from flavour-diagonal or partially flavour off-diagonal equations. A full field-theoretic treatment in the weakly-resonant regime, based on the Kadanoff-Baym (KB) equations, confirms that heavy-neutrino oscillations and mixing are two distinct phenomena, and reproduces the results obtained in our semi-classical framework. Finally, we show that the quasi-particle ansaetze, often employed in KB approaches to RL, discard the phenomenon of mixing, capturing only oscillations and leading to an underestimate of the final asymmetry by a factor of order 2.