Polymer solutions and turbulent superfluids have in common the presence of a complex tangle of lines - macromolecules in the former, quantized vortex lines in the latter - which contribute to the internal friction and viscous pressure of the system and make them typical non-Newtonian fluids. Here we briefly review some recent studies on such tangles and their consequences on the dynamics and thermodynamics of the whole system, using the framework of extended irreversible thermodynamics. For polymer solutions, we deal with the coupling of diffusion and viscous pressure and its effects on the stability of the solution and shear-induced phase separation; for superfluids, we focus our attention on the coupling between heat flux and the vortex tangle, and its consequences on the second sound. Finally, we outline some of the features learned from the comparison of such diverse systems, concerning the contribution of the tangle's geometry to the entropy of the system. (C) 2007 Elsevier B.V. All rights reserved.