Theory and simulations are used to provide understanding of the observed phenomena and to guide the activities in polymer synthesis and assembly. Simulations of polymeric materials and their properties expands over the three scale domains, according to the system size to be modeled and to the time scale of the phenomena sought: (i) the quantum scale for small systems and the femtosecond/picosecond time scale; (ii) the atomistic resolution for larger systems (on the nanometer scale) and longer times from nano- to microseconds time scales, i.e., systems which can be still treated as ensembles of atoms, but which are already too large for a quantum mechanical treatment. This is the domain of molecular dynamics and/or of Monte Carlo simulations; and (iii) the mesoscale for larger systems and long characteristic time of the phenomena of interest, micrometer/(nano)microsecond length/time domain, where a treatment as an ensemble of atoms is not possible.