Consistently atomistic understanding of the mechanism behind the intriguing behavior of low-dimensional systems including monatomic chains, hollow tubes, surface skins, nanocavities, nanowires, and nanograins has long been a high challenge. This article reports recent progress in this regard. A survey is presented and then is followed by analytical approaches in terms of local bond average (LBA) from the perspective of bonding energetics and its functional dependence on external stimuli of coordination environment and temperature change. It is shown that the measurable quantities of a specimen can be functionally correlated to the identities of the representative bonds and their responses to the external stimuli. It is understood that the shortened and strengthened bonds between the under-coordinated atoms and the associated local strain and energy trapping dictate intrinsically the mechanical behavior of systems with large portion of under-coordinated atoms. The thermal softening of a substance arises from thermally-induced bond expansion and lattice vibration that weakens the bonds through the internal energy increase. The competition between the energy-density-gain and the residual atomic cohesive-energy in the relaxed surface skin determines intrinsically the mechanical performance of a mesoscopic specimen, whereas competition between the activation and inhibition of atomic dislocations dominates extrinsically the yield strength of the specimen in plastic deformation.