Low-dimensional carbon nanostructures, such as nanotubes and graphenes, represent one of the most promising classes of materials, in view of their potential use in nanotechnology. However, their exploitation in applications is often hindered by difficulties in their synthesis and purification. Despite the huge efforts by the research community, the production of nanostructured carbon materials with controlled properties is still beyond reach. Nonetheless, this step is nowadays mandatory for significant progresses in the realization of advanced applications and devices based on low-dimensional carbon nanostructures. Although promising alternative routes for the fabrication of nanostructured carbon materials have recently been proposed, a comprehensive understanding of the key factors governing the bottom-up assembly of simple precursors to form complex systems with tailored properties is still at its early stages. In this paper, following a survey of recent experimental efforts in the bottom-up synthesis of carbon nanostructures, we attempt to clarify generalized criteria for the design of suitable precursors that can be used as building blocks in the production of complex systems based on sp(2) carbon atoms and discuss potential synthetic strategies. In particular, the approaches presented in this feature article are based on the application of concepts borrowed from traditional organic chemistry, such as valence-bond theory and Clar sextet theory, and on their extension to the case of complex carbon nanomaterials. We also present and discuss a validation of these approaches through first-principle calculations on prototypical systems. Detailed studies on the processes involved in the bottom-up fabrication of low-dimensional carbon nanostructures are expected to pave the way for the design and optimization of precursors and efficient synthetic routes, thus allowing the development of novel materials with controlled morphology and properties that can be used in technological applications.