This thesis is concerned with vibrational effects in resonant charge transport through molecular junctions. The first research chapter examines the role of non-equilibrium vibrational dynamics in charge transport through a molecular double quantum dot. We demonstrate that non-equilibrium vibrational effects in such a system can result in current suppression and negative differential conductance. The second research chapter describes how vibrational dynamics can be incorporated into the theoretical description of molecular junctions based on a Pariser-Parr-Pople Hamiltonian. As a case study, we consider a prototypical spiro-conjugated molecular junction. We demonstrate that the transport properties of this system are governed by an interplay between destructive quantum interference and Jahn-Teller distortion (an effect of vibronic origin). In the next chapter, we examine the role of collective vibrational coupling in charge transport through a two-site molecular system akin to the one considered in the first research chapter. We demonstrate that such interactions can significantly enhance the efficiency of transport through such a system, and also take this opportunity to analyse various theoretical descriptions of electron-vibrational interactions commonly used in the transport setting. In the fourth research chapter, we consider a single-site molecular system coupled to a collection of thermalised vibrational modes. We formulate a relatively simple yet powerful theoretical framework describing charge transport through such a system. We recover the Marcus and Landauer-Buttiker theories of transport in the limit of high-temperature and vanishing electron-vibrational coupling, respectively. We further show how lifetime broadening can be consistently incorporated into Marcus theory, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. In the last research chapter, elements of this framework are applied to experimental measurements of charge transport through zinc-porphyrin molecular junctions. This joint experimental-theoretical study provides, for the first time, a full understanding of the resonant transport regime of graphene-based molecular junctions.