Carbon nanotubes (both the single- and multi-walled), in the family of nanostructured carbons, are of great interest because of several unsurpassable physical properties and it needs to be shown that they are physically stable and structurally unaltered when subjected to radiation. In addition to testing them for space applications, when exposed to high energy electron beam from transmission electron microscopy, the results seem quite promising in terms of nano-engineering/ nano-manufacturing for producing novel nanocarbons [1-3]. Experimental studies of effects of electron beam irradiation on carbon nanotubes show that multi-walled ones tend to be relatively more robust than their single-walled kins. The increased exposure on an individual bundle of single-wall nanotubes promoted graphitization, pinching, and cross-linking analogous to polymers forming an intra-molecular junction (IMJ) within the area of electron beam focus, possibly through aggregates of amorphous carbon [2,3]. Formation of novel nanostructures (nano-ring and helix-like) due to irradiation are observed. These studies shed light on the dynamics of nanomanufacturing and a regime of possible relevance of these materials for: (i) short-term space missions; (ii) radiation hard programmable logic circuits; and (iii) radiation pressure sensors. It is suggestive that a local reorganization occurs. Through resonance Raman spectroscopy and related techniques we also elucidate an important notion of global topology and curvature at nanoscale which points to an emergent paradigm of Curvature/Topology → Property → Functionality in these technologically important geometries of carbons: nanotubes, fullerenes, nanorings, nanocones, nanohorns and nanodisks. To this end, we have determined the variation in first order high frequency Raman band which indicates a strong electron-phonon coupling. These concepts also apply to nanostructures of other “topological materials” such as BN nanotubes and nanotori, helical gold nanotubes as well as Möbius conjugated polymers.