This dissertation is dedicated to the study of the tunnel effect in van der Waals heterostructures assembled from two-dimensional crystals of various materials. It is devoted to exploring three conceptually different systems; (i) graphene-hexagonal boron nitride-graphene tunnel transistors, (ii) graphene-two dimensional ferromagnetic semiconductor-graphene junctions, (iii) graphene-hexagonal boron nitride-two dimensional superconductor junctions. The field-effect vertical tunnel transistors constructed of atomically thin graphene and hexagonal boron nitride layers are an exceptional platform for the study of various resonant mechanisms due to their outstanding synergetic properties. Here, we report on the realization of (a) the inelastic phonon-assisted resonant tunnelling process, (b) sequential resonant tunnelling apparatus through the localized electronic states of hexagonal boron nitride, and most important, (c) the twist controlled resonant tunnelling process for vertical transistors, which consists of monolayer/bilayer graphene. The latter is prompted by the precise crystallographic alignment of graphene layers, where the momentum mismatch between the Dirac cones is compensated by the energy obtained from the electrostatic field. Notably, the momentum of tunnelling electrons is conserved within such an event, therefore, owing to a peculiar property of graphene, the momentum-pseudospin coupling, it was possible to both directly visualize and control the chiral quantum state of electrons (holes), which is of a fundamental importance for graphene physics. Recently, the family of two-dimensional materials has been expanded to include both ferromagnetic semiconductors and unconventional superconductors. Here, we show that a few layers of exfoliated CrBr3 are ferromagnetic by characterizing functional tunnel devices, where a CrBr3 layer is sandwiched in-between graphene electrodes. We report on a new type of tunnelling mechanism in van der Waals heterostructures by demonstrating that electrons in such a junction are tunnelling with the help of an emission (and, at high temperature, absorption) of magnons within the CrBr3 layer. We also show that NbSe2 remains superconducting down to the thickness of a monolayer, by electrical measurements of graphene-hexagonal boron nitride-NbSe2 tunnel junctions, where in particular, we demonstrate a fully developed gap that is rapidly reduced with the layer thickness.