Carbon nanostructures (CNS) constitute an important class of materials derived from graphene that share remarkable photophysical and photochemical properties of potential interest for a number of technological applications, ranging from electron transport and spintronics to heat conduction and solar energy conversion. In this work, we use linear-response time-dependent density functional theory (LR-TDDFT) for the calculation of spinorbit couplings (SOC) and intersystem crossing transitions in a number of CNS including: 0D quantum dots (C60 and graphene nanoflakes), 1D carbon nanotubes, and 2D graphene. The method developed in [J. Chem. Phys. 2014, 140, 144103] and [J. Chem. Phys. 2015, 143, 224105] is able to capture the dependence of the SOC values on subtle electronic structure differences characterizing the different 0D, 1D, and 2D CNS and on geometrical properties such as curvature and topological indices of carbon nanotubes. Compared to tight-binding calculations, our first-principles approach is able to reproduce very accurate results without the need of any ad-hoc parametrization. When combined with nonadiabatic dynamics, SOC can be used to compute intersystem crossing transitions between states of different spin multiplicities, opening new avenues in the study of the complex dynamics of photoexcited CNS. In particular, we analyze the dependence of the intersystem crossing rates on thermal structural fluctuations in a carbon nanoflake.