Hyperbolic metamaterials are a class of artificial (nano-) structures, designed to transport electric fields, which would otherwise evanescently decay in free space. Field profiles of evanescent waves can be well matched to profiles of surface plasmons - confined metal-dielectric boundary surface charge oscillations - allowing resonant coupling between them. By building a structure, composed of alternating metal-dielectric boundaries, one can ensure transportation of the evanescent modes across a whole stack of layers. Here we employ graphene monolayers as conductive media, alternating with dielectric spacers. To ensure an accurate non-local description, necessary for high-k evanescent modes, we use a non-local quantum conductivity model for graphene, which accounts for inter- and intra-band transition processes and temperature effects, thus facilitating a comprehensive loss and gain description. Here we present and formalise the theory of graphene-based passive and active hyperbolic metamaterials. We discuss the developed theoretical ’toolset’, used to describe hyperbolic properties of graphene-based metamaterials, such as plasmonic regions, band structure, tunability etc. With our toolset, we theoretically predict the possibility of using graphene-based hyperbolic metamaterials for plasmonic loss compensation and amplification and demonstrate the possibility of using active and passive stacks with finite number of layers to propagate and amplify Gaussian pulses. In the second part of this thesis we propose to employ Moiré patterns, arising from the structural interference between single layers of graphene and hexagonal Boron Nitride. This bi-layer forms an effective metasurface which can be designed to facilitate coupling of vacuum plane waves to high-k plasmon modes of graphene. Using the extinction theorem, we model Moiré patterns as sinusoidal gratings with a period and depth, corresponding to those, experimentally observed. We show that a reflectivity drop of ∼ 0.5% can be achieved with the help of this metasurface, placed on the boundary between a (Drude) metal and a dielectric structure.