Nanostructures can have interesting waveguide properties at very high frequencies in the order of Tera-Hertz. At such high frequencies, continuum model based methods cannot be adopted due to their limitation of the size with respect to the wavelength, which is very small at such frequencies. The length scales of nanostructures are often sufficiently small, and hence for the applicability of classical continuum models, we need to consider the small length scales such as lattice spacing between individual atoms, grain size, etc. The conventional continuum models cannot handle scale effects. Hence the best alternative is to use those methods which provides the simplicity of continuum models and at the same time incorporate the effects of scale in such chosen continuum models. This makes a physically consistent classical continuum model formulation very challenging. The nonlocal elasticity theory is useful tool in treating phenomena whose origins lie in the regimes smaller than the classical continuum models. Such nonlocal continuum mechanics based theories have been applied to study the wave propagation properties in nanostructures in the present book.