  We briefly review the recent advances in the rheology of entangled polymers
and identify emerging research trends and outstanding challenges, especially
with respect to branched polymers. Emphasis is placed on the role of
well-characterized model systems, as well as the synergy of
synthesis-characterization, rheometry and modeling/simulations. The theoretical
framework for understanding the observed linear and nonlinear rheological
phenomena is the tube model which is critically assessed in view of its
successes and shortcomings, whereas alternative approaches are briefly
discussed. Finally, intriguing experimental findings and controversial issues
that merit consistent explanation, such as shear banding instabilities,
multiple stress overshoots in transient simple shear and enhanced steady-state
elongational viscosity in polymer solutions, are discussed, whereas future
directions such as branch point dynamics and anisotropic monomeric friction are
outlined.
