Polymer nanocomposites refer to a broad range of composite materials with polymer acting as the matrix and any nanomaterial acting as the filler. Due to unprecedented improvement observed in properties of the nanocomposites, research interest in this area has grown exponentially in recent years. In designing better nano-composites for advanced technological applications we face several major challenges. In this book, we have utilized first principle calculations, atomistic simulations, coarse-grained modeling and constitutive equations to develop structure-property relationships for an amorphous aromatic piezoelectric polyimide substituted with nitrile dipole, carbon nanotubes and resulting nanocomposites. In particular we have studied the thermal, mechanical and dielectric properties of the polyimide, nanotube and their nanocomposites through multi-scale modeling technique. Notably, we have investigated the time dependent response of these highly complex polymers, to our best knowledge this is the first of its kind. We expect the results obtained and understanding gained through modeling and simulations may be used in guiding development of new nanocomposites.