In this talk I shall present and discuss, from physical and mathematical viewpoint, a number of Non-Newtonian models that are frequently used (with different aims) in engineering and mathematical communities. In particular, I shall try to direct the attention of the interested applied mathematician toward the main reason why these models were originally introduced, that is, to explain experiments that the Navier-Stokes model was not able to predict. In fact, it turns out that many among the classical experiments still lack an explanation on a solid mathematical basis, and they certainly represent an exciting challenge for the interested mathematician.