## 1 Introduction  
At the turn of the century, a new field of research emerged that was a hybrid of physics, electrical engineering, and materials science. The study of metamaterials (MMs) addresses the rational design and arrangement of a material's building blocks to attain physical properties that may go significantly beyond those of its original constituent materials. Most often, the concept of MMs is associated with electromagnetic (EM) wave propagation, where the engineering of resonant subwavelength structures allows for the precise control of effective wave properties. It is this advanced functionality that enables the realization of unique wave phenomena, such as the focusing of light below the diffraction limit or EM cloaking of objects--concepts that have captured the imagination of researchers and the general public alike. Importantly, the element of functionality is an integral part of the MM concept.  
Recently, propagation of EM waves on two-dimensional interfaces has stimulated tremendous interest [1; 2]. Surface plasmonic polariton (SPP) [3; 4; 5; 6] attracts lots of attention in the scientific community. SPPs have provided a fertile ground for new applications in many fields [7; 8; 9; 10; 11; 12; 13; 14]. During last several decades, it has been demonstrated that it is possible to control SPPs in an unprecedented way by nanostructuring the metal surface. Hyperbolic MMs [15] have stimulated increasing interest because of the capability of supporting large wavenumbers. Their unusual properties opened wide avenues for many fascinating applications, such as hyperlenses for biosensing [9]. The potential biosensing applications are achievable with the novel high-frequency cut-off SPPs in hyperbolic graphene-dielectric multilayered metamaterials. For infrared frequencies, infrared plasmonic MMs were designed by [PERSON] et al. Moreover, their use has been suggested as a biosensing platform [16]. It is worthwhile to note that hyperbolic MMs have already been treated from the perspective of supporting photonic modes with unbounded k-vectors in [17]. Herein, we take a step forward by investigating various types of modes supported by multilayered structures, for example, Ferrell-Berreman (FB) and others. The former is achievable by employing the tunability properties of the graphene used as a building block of the multilayered composite. The experimental realization of a multilayered structure of alternating graphene and Al\({}_{2}\)O\({}_{3}\) layers has been reported in [18]. However, the former study does not offer an overview of the tuning possibilities.  
Our present discussion of multilayered MMs is divided into three parts. In the first part, fundamental physical notions that underlie graphene-dielectric multilayered MMs are discussed. Moreover, the realization of the dispersion characteristics of the SPPs, their theoretical implications, and their specific characteristics are reviewed. In addition, the concept of FB modes is introduced. In Section 4, the extension of the frequency region of the SPPs is discussed in terms of the inclusion of a third additional layer. Particular emphasis is placed on the topological structures. Finally, Section 5 discusses the possibility of the inclusion of transparent-conducting oxide (TCO) layers in multilayered MMs, specifically paying attention to the new kinds of the SPPs.