The concept of the generalized Newtonian fluid (GNF) provides a useful basis for the formulation of constitutive equations for real materials. The purpose of this paper is to review the rational foundations of the generalized Newtonian fluid, and to discuss the problems involved in its practical application to real materials. Of special interest are the types of material constants which must appear and the dimensionless groups which govern the solutions of boundary value problems. It is demonstrated that, if the material function of a GNF contains one material constant with units of viscosity, it must also contain at least one material constant with units of time (or reciprocal time). The role of this characteristic time for both purely-viscous and elastic fluids is discussed.