The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on singlephase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2437-2767, 2010