Abstract: This thesis presents, in its first part, an investigation on the trembling motion of wave packets known as zitterbewegung (ZBW), in multilayer graphene, as well as in moiré excitons in twisted MoS2/WSe2 hetero-bilayers. In the last few decades, the dynamics of wave packets has been subject of many theoretical and experimental studies in various types of systems such as semiconductors, superconductors, crystalline solids and cold atoms. The discovery of graphene and moiré excitons in twisted hetero-bilayers, brought two new platforms for the investigation on time evolution of wave packets and possible observation of ZBW. This trembling motion was first theoretically predicted by Schrödinger for wave packets describing particles that obey the Dirac equation. This is exactly the case of low energy electrons in graphene, as well as of moiré exciton in twisted MoS2/WSe2 under an external applied electromagnetic field. ZBW in multilayer graphene was studied both analytically and computationally, respectively, through the Green's function and split-operator methods. In this system, it is found that ZBW depends not only on the wave packet width and initial pseudospin polarization, but also on the number of layers. Furthermore, the analytical and numerical methods proposed here allow to investigate wave packet dynamics in graphene systems with an arbitrary number of layers and arbitrary potential landscapes. For moiré excitons in twisted MoS2/WSe2 hetero-bilayers, it is shown that, analogously to other Dirac-like particles, this system also exhibits ZBW when under a perpendicular applied field. In this case, the ZBW presents long timescales that are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moiré excitons in van der Waals heterostructures as an advantageous solidstate platform to probe zitterbewegung, broadly tunable by gating and inter-layer twist angle. In the second part of this thesis, a study into graphene plasmonic in van der Waals heterostructure (vdWhs) are treated in a linear response framework within the Random Phase Approximation and with support of the quantum electrostatic heterostructure (QEH), a DFT-based method. Since Dirac plasmons in graphene are very sensitive to the dielectric properties of the environment, it is possible to explore this property to probe the structure and composition of van der Waals heterostructures (vdWh) placed underneath a single graphene layer. In this way, one can achieve a layer sensitivity of a single layer and differentiate between different TMDs for heterostructures thicker than 2 layers. As a consequence of this, study, the hybridization of Dirac plasmons in graphene with phonons of transition metal dichalcogenides (TMDs), when the materials are combined in so-called van der Waals heterostructures (vdWh) forming surface plasmon-phonon polaritons (SPPPs) are also investigated. It was found that it is possible to realize both strong and ultrastrong coupling regimes by tuning graphene’s Fermi energy and changing TMD layer number.