The Doi-Edwards (D-E) molecular, viscoelastic theory for entangled polymers is used as the framework for an experimental study of flow anomalies in well-characterized polymer solutions and melts, spanning a wide range of entanglement densities. Results of linear viscoelastic and nonlinear rheology experiments -- steady and step shear were compared to existing theory. Unlike weakly and moderately entangled polymers (N/N sub(e) less than and equal to 11), the step-shear damping function, h (upsilon) = G (t, upsilon)/ G (t, upsilon-0), for polymers with high entanglement densities is more strain softening than the Doi-Edwards prediction, h sub(D-E (upsilon)). Two likely causes of this deviation, commonly called type C Damping, are interfacial slip and shear banding. To isolate the mechanism(s) responsible for the discrepancy, we combine macroscopic techniques (rheometry) with direct visualization (confocal microscopy and particle image velocimetry) during steady shear flow. In the latter case, this high resolution measurement technique allows us to construct the velocity profile in narrow-gap, planar-Couette shear flow. Importantly, even for shear rates well into the non-Newtonian shear-rate regime, where the unmodified D-E theory predicts shear banding, all the shear profiles are found to be linear. There is strong evidence of interfacial slip, which can be characterized and compared to slip theories for entangled polymers. To remove/ weaken the role of slip, the original confocal set-up was modified to allow both a transient shear and large-gap study. These results were compared with qualitative expectations from transient constitutive curves: sigma (upsilon ) vs. upsilon , measured at similar times in mechanical rheometry experiments. During start-up of steady shear flow, rheometry measurements show a maximum in sigma (upsilon ) vs. upsilon at times prior to steady state. To determine whether this transient, non-monotonic stress growth leads to transient shear banding, we characterized the velocity profile as a function of time. Surprisingly, these measurements again yield decidedly linear profiles that vary little with time, indicating that there is some feature of the shear flow that stabilizes it against banding. Finally, step shear experiments with entangled star-branched polymer solutions reveal that the damping function is universal but different from h sub(D-E (upsilon)). And, linear and nonlinear rheology of unentangled stars indicates that their flow behavior follows Rouse model predictions. . . . .