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The region between the infrared and microwave region in the electromagnetic spectrum, the Terahertz (THz) gap, provides an exciting opportunity for future wireless communications as this band has been under utilised. This doctoral work takes a two-pronged approach into closing the THz gap with low-dimensional materials. The first attempt addresses the need for a compact THz source that can operate at room temperature. The second approach addresses the need to build optical elements such as filters and modulators in the THz spectrum. Terahertz quantum cascade lasers (THz QCLs) are one of the most compact, powerful sources of coherent radiation that bridge the terahertz gap. However, their cryogenic requirements for operation limit the scope of the applications. This is because of the electron-electron scattering and heating of the 2-dimensional free electron gas which leads to significant optical phonon scattering of the hot electrons. Theoretical studies in laterally confined QCL structures have predicted enhanced lifetime of the upper state through suppression of the non-radiative intersubband relaxation of carriers, which leads to lower threshold, and higher temperature performance. Lithographically defined vertical nanopillar arrays with electrostatic radius less than tens of nm offer a possible route to achieve lateral confinement, which can be integrated into QCL structures. A typical gain medium in a QCL consists of at least 100 repeat periods, with a thickness of 6-14 micron. For practical implementation of the top-down approach, restrictions are imposed by aspect ratios that can be achieved in present dry-etching systems. Typically, for sub-200 nm radius pillars, the thickness ranges from 1-3.5 micron. It is therefore necessary to work with THz QCLs based on 3-4 quantum well active regions, so as to maximise the number of repeat periods (hence gain) within an ultra-thin active region. After an introductory chapter, Chapter 2 presents a theoretical treatise on the realistic electrostatic potential in a lithographically defined nanopillar by scaling from a single quantum well (resonant tunnelling diode) to a THz QCL. Chapter 2 also discusses, the effect of lateral confinement on the intersubband states and the plasmonic mode in a THz QCL. One of the key experimental challenges in scaling down from QCLs to quantum-dot cascade lasers is the electrical injection into the nanopillars. This involves insulation and planarisation of the high aspect-ratio nanopillar arrays. Furthermore, the choice of the planarising layer is critical since it determines the loss of any optical mode. This experimental challenge is solved in Chapter 3. Chapter 4 presents the electro-optic performance of low-repeat period QCLs with an active region thickness that is less than 3.5 micron. Another topic of recent interest in the THz optics community is plasmonics in graphene. This is because the bound electromagnetic modes (plasmons) are tightly confined to the surface and can also be tuned with carrier concentration. Plasmonic resonance at terahertz frequencies can be achieved by gating graphene grown via chemical vapour deposition (CVD) to a high carrier concentration. THz time domain spectroscopy of such gated monolayer graphene shows resonance features around 1.6 THz superimposed on the Drude-like frequency response of graphene which may be related to the inherent poly-crystallinity of CVD graphene. Chapter 5 discusses these results, as an understanding of these features is necessary for the development of future THz optical elements based on CVD graphene. Chapter 5 finally describes how the gate tunability of THz transmission through graphene can be exploited to indirectly modulate a THz QCL. Chapter 6 presents ideas from this doctoral work, which can be developed in future to address the issues of enhanced temperature performance of THz QCLs and to realise realistic THz devices based on graphene.