[[File:Viscous regimes chart.png|thumb|right|320px|Viscosity, the slope of each line, varies among materials]]
Newton's law of viscosity is a [[constitutive equation]] (like [[Hooke's law]], [[Fick's law]], [[Ohm's law]]): it is not a fundamental law of nature but an approximation that holds in some materials and fails in others.
A fluid that behaves according to Newton's law, with a viscosity ''μ'' that is independent of the stress, is said to be [[Newtonian fluid|Newtonian]]. [[Gas]]es, [[water]] and many common liquids can be considered Newtonian in ordinary conditions and contexts. There are many [[non-Newtonian fluid]]s that significantly deviate from that law in some way or other. For example:
*[[Shear thickening]] liquids, whose viscosity increases with the rate of shear strain.
*[[Shear thinning]] liquids, whose viscosity decreases with the rate of shear strain.
*[[Thixotropic]] liquids, that become less viscous over time when shaken, agitated, or otherwise stressed.
*[[Rheopectic]] liquids, that become more viscous over time when shaken, agitated, or otherwise stressed.
*[[Bingham plastic]]s that behave as a solid at low stresses but flows as a viscous fluid at high stresses.
Shear thinning liquids are very commonly, but misleadingly, described as thixotropic.
Even for a Newtonian fluid, the viscosity usually depends on its composition and temperature. For gases and other [[compressible fluid]]s, it depends on temperature and varies very slowly with pressure.
The viscosity of some fluids may depend on other factors. A [[magnetorheological fluid]], for example, becomes thicker when subjected to a [[magnetic field]], possibly to the point of behaving like a solid.