As a new class of materials, carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) have been continuing fascinating the community with properties that can be seen from neither bulk graphite nor diamond. Although the physics and chemistry of these carbon allotropes have been intensively investigated from various perspectives, the laws governing the fascinations and their interdependence remain as yet undetermined. From the perspectives of bond and nonbond formation, dissociation, relaxation, vibration, and the associated energetics and dynamics of charge repopulation, polarization, densification, and localization, this article aims to show that the broken-bond-induced local bond contraction and bond strength gain, quantum entrapment and densification of charge and energy, polarization of the unpaired edge dangling σ-bond electrons, and the formation of the pseudo-π-bond between the dangling σ-bond electrons along the edges are responsible for the anomalies. Theoretical reproduction of the experimentally observed elastic modulus enhancement, melting point depression, layer-number, strain, pressure and temperature induced Raman shift, C 1s core-level positive shift, work function reduction, band gap expansion, edge and defect selective generation of the Dirac-Fermi polarons and the associated magnetism consistently confirmed that the shorter and stronger bonds between undercoordinated carbon atoms modulate locally the atomic cohesive energy, the Hamiltonian, and hence the detectable bulk properties. The polarization of the unpaired dangling σ-bond electrons by the densely, deeply, and locally entrapped core and bonding electrons generates the massless, magnetic and mobile Dirac-Fermi polarons at sites surrounding vacancies and zigzag-GNR edges. The pseudo-π-bond formation between the nearest dangling σ-bond electrons along the armchair-GNR and the reconstructed zigzag-GNR edges discriminates them from the zigzag-GNR edges or vacancies in the electronic and magnetic properties. Consistency between predictions and observations confirmed that the C–C bond contracts by up to 30% with a 152% bond strength gain at the edges with respect to those in the bulk diamond.