Study of complex macromolecular systems through molecular simulations is a very intense research area. Here we present an overview concerning the development and application of hierarchical particle coarse-graining molecular dynamics simulations on the quantitative prediction of the dynamics and the rheology of polymers. Through a systematic time mapping approach that involves data from detailed atomistic dynamic simulations the coarse-grained polymer model can be used to quantitatively predict the dynamics and the rheology of the polymeric chains in a very broad range of characteristic length and time scales. Data from the application of these approaches on the dynamics of polystyrene melts under equilibrium and under shear flow conditions are presented.