What is the difference between Newtonian and non-Newtonian fluids?

Newtonian fluids have constant viscosity regardless of shear rate - shear stress is directly proportional to shear rate (water, most gases, light oils). Non-Newtonian fluids have viscosity that varies with shear rate: shear-thinning (pseudoplastic - viscosity decreases with shear, like paint, polymer solutions), shear-thickening (dilatant - viscosity increases, like cornstarch slurry), Bingham plastic (requires yield stress to flow, like toothpaste), and thixotropic (time-dependent thinning). Non-Newtonian behavior affects pump selection and piping design.