This book presents the main results obtained by different laboratories involved in the research group Rheology for polymer melt processing which is associated with French universities, schools of engineering, and the CNRS (Centre National de la Recherche Scientifique-France). The group comprises some 15 research laboratories of varied disciplines (chemistry, physics, material sciences, mechanics, mathematics), but with a common challenge viz. to enhance the understanding of the relationships between macromolecular species, their rheology and their processing. Some crucial issues of polymer science have been addressed: correlation of viscoelastic macroscopic bulk property measurements and models, slip at the wall, extrusion defects, correlation between numerical flow simulations and experiments. Features of the book: The book is unique in that it allows one to grasp the key issues in polymer rheology and processing at once through a series of detailed state-of-the-art contributions, which were previously scattered throughout the literature. Each paper was reviewed by experts and the book editors and some coordination was established in order to achieve a readable and easy access style. Papers have been grouped in sections covering successively: Molecular dynamics, Constitutive equations and numerical modelling, Simple and complex flows. Each paper can be read independently. Since the book is intended as an introduction to the main topics in polymer processing, it will be of interest to graduate students as well as to scientists in academic and industrial laboratories.