This thesis presents research that has been driven towards the exploration and exploitation of the fundamental inter-atomic interactions in low-dimensional crystalline materials like nanotubes and graphene. A special focus has been maintained on understanding their mechanical behavior which is directly related to the strength of these interactions as well as their structural arrangement. Thus, allowing one to explain not only their high strength but also their fatigue behavior. Another important aspect about these interactions is how they can be manipulated to synthesize materials with high crystallinity or with purposeful ordering of defects. This led to the investigation of strategies that, for example, allow growth of infinitely large single crystals of graphene, which are virtually defect free. On the other hand, if the growth substrate is allowed to curve controllably, the work showed how defects can be created in a deterministic way. Therefore, a key aspect of the research presented in this thesis has been to understand the structure-property correlations, which affect the nanomechanics and growth of these materials.