New paradigms in materials and devices lead to new technologies, which are necessary for continued scientific progress. We have determined, in foundational studies, that nonlinear nanostructures, such as carbon nanotube based helices and coils, may be synthesized through the use of specific catalysts in chemical vapor deposition and could open up new vistas in electrical, mechanical, and optical engineering, e.g. as electrical inductors, nanoscale mechanical springs, and metamaterials. First, a thermodynamic model based on exclusion volume principles common in chemical and biological systems that could potentially explain coiling in nanostructures, will be introduced. The crucial role of the interactions between specific catalyst particles, e.g. indium and tin, and the growing nanostructure for coil growth, which has been verified through experiment, will be elucidated. The talk will be concluded with a brief exposition on the unique applications of these structures, say in localized energy absorption and electromagnetic radiation coupling.