Graphene-based nanostructures, such as 1D graphene nanoribbons [1-4], and graphene-related 2D materials, such as C3N [5-7], offer extraordinary versatility as next-generation semiconductors for nanoelectronics, optoelectronics and energy devices (e.g. batteries) [8,9], due to their tunable properties, including charge-carrier mobility, optical absorption, excitonic features, electronic bandgap and mechanical properties which are uniquely defined by their chemical structure.We here adopt predictive first-principles computational schemes - based on both density-functional theory and many-body perturbation theory - to acquire a comprehensive understanding of the electronic, optical and vibrational (Raman and IR) excitations of such low-D graphene-based materials, as a function of their structure, functionalization, distortion, and different reaction stage in their fabrication. Our results, often combined to experimental investigations, allow not only to fingerprint their precise structures, but also to physically interpret and predict their spectral features also in view of a material design perspective. N. Cavani, M. De Corato, A. Ruini, D. Prezzi, E. Molinari, A. Lodi Rizzini, A. Rosi, R. Biagi, V. Corradini, X.Y. Wang, X. L. Feng, A. Narita, K. Mullen, V. De Renzi, “Vibrational signature of the graphene nanoribbon edge structure from high-resolution electron energy-loss spectroscopy”, Nanoscale 12, 19681-19688 (2020)D. Rizzo, D. Prezzi, A. Ruini, V. Nagyte, A. Keerthi, A. Narita, U. Beser, F.G. Xu, Y,Y, Mai, X.L. Feng, K. Mullen, E. Molinari, C. Casiraghi, “Multiwavelength Raman spectroscopy of ultranarrow nanoribbons made by solution-mediated bottom-up approach”, Phys. Rev. B 100, 045406 (2019)B. Hu, P. Xie, M.De Corato, A. Ruini, S. Zhao, F. Meggendorfer, L.A. Straaso, L. Rondin, P. Simon, J. Li, J.J. Finley, M.R. Hansen, J.S. Lauret, E. Molinari, X.L. Feng, J.V. Barth, C.A. Palma, D. Prezzi, K. Mullen, A. Narita, “Bandgap Engineering of Graphene Nanoribbons by Control over Structural Distortion”, J. Am. Chem. Soc.140, 7803-7809 (2018)R. Denk, M. Hohage, P. Zeppenfeld, J. M. Cai, C. A. Pignedoli, H. Sode, R. Fasel, X. L. Feng, K. Mullen, S. D. Wang, D. Prezzi, A Ferretti, A. Ruini, E. Molinari, P. Ruffieux, “Exciton-dominated optical response of ultra-narrow graphene nanoribbons”, Nature Communications 5, 4253 (2014).M. Zanfrognini, M. Bonacci, F. Paleari, E. Molinari, A. Ruini, A. Ferretti, M. J. Caldas, D. Varsano, “Quenching of low-energy optical absorption in bilayer polytypes”, Physical Review Materials 7 (6), 064006 (2023)M. Zanfrognini, N. Spallanzani, M. Bonacci, E. Molinari, A. Ruini, M.J. Caldas, A. Ferretti, D. Varsano, “Effect of uniaxial strain on the excitonic properties of monolayer: A symmetry-based analysis”, Physical Review B 107 (4), 045430 (2023)M. Bonacci, M. Zanfrognini, E. Molinari, A. Ruini, M. J Caldas, A. Ferretti, D. Varsano, “Excitonic effects in graphene-like C3N”, Phys. Rev. Mat. 6, 034009 (2022)M. A. Salvador, R. Maji, F. Rossella, E. Degoli, A. Ruini, R. Magri, “Structural and Dynamic Characterization of Li–Ionic Liquid Electrolyte Solutions for Application in Li-Ion Batteries: A Molecular Dynamics Approach”, Batteries 9 (4), 234 (2023)R. Maji, M. A. Salvador, A. Ruini, R. Magri, E. Degoli, “A first-principles study of self-healing binders for next-generation Si-based lithium-ion batteries”, Materials Today Chemistry 29, 101474 (2023)