For the past three decades, newly discovered carbon nanostructures such as fullerenes, graphene and carbon nanotubes (CNTs) have revolutionized the field of nanoscience, introducing many practical and potential applications pertaining to their exceptional structural, mechanical, thermal, and optoelectronic properties. Raman spectroscopy has been an instrumental technique for characterizing these materials due to its non-destructive nature and high sensitivity to the material responses. While Raman spectroscopy is broadly used for identifying specific material types and quality, it has also been increasingly useful as a tool for probing the electronic and excitonic properties, as well as their interplay with the vibrational properties in the aforementioned carbon nanomaterials. In this dissertation, we present our Raman-related research on carbon nanotubes and a new member of the nano-carbon family - carbon nanohoops (cycloparaphenylenes, or CPPs). We discuss our new findings on the resonance Raman spectroscopy (RRS) of various semiconducting CNTs, with the focus on the Raman excitation profiles (REPs) for the G-band. The asymmetric lineshapes observed in the G-band REPs for the second excitonic (E22) transition of these CNTs contradict a long-held approximation, the Franck-Condon principle, for the vibronic properties of the carbon nanotubes. In addition, the G-band REPs from the closely spaced E33 and E44 transitions are investigated, and we demonstrate that these excitonic levels exhibit significant quantum interference effects between each other. We also present the first comprehensive study of Raman spectroscopy of CPPs. Analogously to CNTs, we show that Raman spectroscopy can be used to identify CPPs of different sizes. A plethora of Raman modes are observed in these spectra, including modes that are comparable to those of CNTs, such as the G-band, as well as Raman peaks that are unique for CPPs. Calculated Raman spectra using density functional theory (DFT) are compared with the experimental results for the assignment of different modes. Furthermore, we refine our knowledge of the CPP Raman modes by concentrating on the even-numbered CPPs. By taking advantage of the symmetry arguments in the even [n]CPPs, we are able to utilize group theory and accurately identify the size dependences of different Raman-active modes.