Control of key technological and benchmark flows of polymer fluids poses a number of challenges. Some of them are nowadays under active investigation and rather far from complete understanding. This review considers such phenomena as both practically important and governed by fundamental laws of rheology and non-linear fluid mechanics. We observe, shear bands in polymeric and other complex structured fluids (like wormlike micellar solutions or soft glassy materials), birefrigerent strands, peculiarities of stress and pressure losses in fluids moving through complex shape domains. These and other processes involve inhomogeneity, instabilities and transient modes creeping in flow fields. In practical aspect this is of interest in such industrial process as polymer flooding for Enhanced Oil Recovery (EOR), where a flow inhomogeneity affects a polymer solution injectivity and residual oil saturation. The value of viscoelasticity in the polymer flooding is estimated. The observation is concluded by some new results on relation between polymer concentration in solutions and viscoelastic traits of benchmark flows.
