We discuss boundary layers arising in the high Weissenberg number limit of viscoelastic flows and the scalings that arise in analyzing them. Two quite distinct mechanisms for the formation of viscoelastic boundary layers exist: One mechanism is analogous to that of the Prandtl boundary layer and is linked to the enforcement of the no-slip boundary condition. The other mechanism has nothing to do with the no-slip condition, but is linked to long memory which manifests itself in different stresses near the wall versus some distance from the wall. In certain situations, these stress boundary layers may be embedded within Prandtl type boundary layers. (c) 2012 Elsevier B.V. All rights reserved.