At the level of fundamental science, it was recently demonstrated that molecular wires can mediate long-range phase-coherent tunnelling with remarkably low attenuation over a few nanometre even at room temperature. Furthermore, a large mean free path has been observed in graphene and other graphene-like two-dimensional materials. These create the possibility of using quantum and phonon interference to engineer electron and phonon transport through nanoscale junctions for a wide range of applications such as molecular switches, sensors, piezoelectricity, thermoelectricity and thermal management. To understand transport properties of such devices, it is crucial to calculate their electronic and phononic transmission coefficients. The aim of this tutorial article is to outline the basic theoretical concepts and review the state-of-the-art theoretical and mathematical techniques needed to treat electron, phonon and spin transport in nanoscale molecular junctions. This helps not only to explain new phenomenon observed experimentally but also provides a vital design tool to develop novel nanoscale quantum devices.