Over the past few decades, nanostructures have garnered significant attention due to their potential for embodying new physical paradigms and delivering cutting-edge technological applications. Dimensionality strongly affects the vibrational, electron-phonon, and transport properties of materials by carrying unique and profound signatures that are key to spectroscopic characterization and, more generally, to the future of nanotechnology. This thesis aims to contribute to the general progress in understanding and predicting from first principles these dimensionality signatures. To achieve this goal, we combine analytical modeling and algorithmic development, as well as automation techniques targeting high-throughput calculations.