Different possible mechanisms of non-Newtonian behavior of polymeric and multi-component materials in shearing are discussed. There are two main types of the non-Newtonian media: fluids with the maximal (zero-shear-rate) Newtonian viscosity and yielding visco-plastic materials. Numerous intermediate and superimposing situations can also exist. The main concept of the non-Newtonian viscosity of such elastic fluids as polymer melts is based on definition of their "structure" as the set of relaxation modes modified by deformation. Shear-induced relaxation spectrum transformations lead to non-linearity, formation of anisotropic structures, and changes in the macromolecule entanglement topology. A general approach to quantitative description of non-Newtonian flow of polymer melts is achieved if to assume that the dominant reason of non-linear flow properties is molecular-weight distribution of polydisperse polymers with continuous flow-to rubbery transition from the side of slow relaxation modes with increasing shear rate. The non-Newtonian viscosity of such multi-component systems as numerous suspensions, emulsions, and mixtures is characterized by transition from the flow curves with the zero-shear-rate viscosity to the yield-type behavior. The latter is the direct evidence of a spatial structure which changes in shearing. The yield stress value can be rigorously determined only for rigid structures. For soft matters, the structural breakdown/buildup processes are a time dependent (thixotropic/rheopectic) phenomenon, and the concept of yielding becomes uncertain. Nature of structures in various multi-component materials can be very different but just their existence determines a possibility of non-linear effects in shearing. A special type of the non-Newtonian flow is instability and inhomogeneity of a stream. Different forms of these phenomena (shear banding, layered flow, surface distortions, periodic oscillations, concentration separation, and movement of large structural aggregates) are known. In such situations, the "measured" non-Newtonian viscosity can appear an artifact depending on the size factor. (C) 2012 Elsevier B.V. All rights reserved.