The last two decades have witnessed a tremendous growth in the development and understanding of ${sp}^2$ carbon-based nanostructures. The impact of this research has led to a number of fundamental discoveries that have played a central role in the understanding of many aspects of materials physics and their applications. Much of this progress has been enabled by the development of new techniques to prepare, modify, and assemble low-dimensional materials into devices. The field has also benefited greatly from much progress in theoretical and computational modeling, as well as from advances in characterization techniques developed to probe and manipulate single atomic layers, nanoribbons, and nanotubes. Some of the most fundamental physical properties of ${sp}^2$ carbon-based nanostructures are reviewed and their role as model systems for solid-state physics in one and two dimensions is highlighted. The objective of this review is to provide a thorough account on current understanding of how the details of the atomic structure affect phonons, electrons, and transport in these nanomaterials. The review starts with a description of the behavior of single-layer and few-layer graphene and then expands into the analysis of nanoribbons and nanotubes in terms of their reduced dimensionality and curvature. How the properties can be modified and tailored for specific applications is then discussed. The review concludes with a historical perspective and considers some open questions concerning future directions in the physics of low-dimensional systems and their impact on continued advances in solid-state physics, and also looks beyond carbon nanosystems.

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• Carbon-based materials
• Nanostructures
• Raman spectroscopy