The last twenty years have seen an extraordinary development and application of new modelling concepts and powerful simulation tools in the field of polymers, which have dramatically extended our understanding of structure-property relationships and impacted the design of these materials. This book provides a comprehensive overview of the theory and practice of polymer multiscale modelling methods with a balanced combination of breadth and depth. After introducing the key methods for modelling polymeric materials computationally at the atomistic and mesoscopic levels, the text discusses how bridges between different levels of modelling can be built with minimal loss of predictive ability. It presents the statistical mechanical foundations of these methods and explains how they should be implemented in order to understand and reliably predict structure and dynamics in systems of chain molecules. The book also covers the multitude of real world applications of these methods in polymer science ranging from chain conformation and packing, equilibrium volumetric behaviour, segmental dynamics and terminal relaxation in polymer melts to elastic constants, plasticity, and structural relaxation in polymer glasses, phase equilibria of polymer-solvent systems and miscibility of blends, microphase separation and morphology development in block copolymers and viscoelasticity of unentangled and entangled melts.