abstract: Second gradient fluids (which are different from second grade fluids) are fluids in which the total power expenditure depends on the second derivatives of the velocity field. They are used in a variety of models, from numerical analysis to complex fluid mechanics. Indeed, they are not just a model. Well, yes, they are, but in some sense they represent the simplest generalisation of a simple fluid, and also in the linear case they can be useful to describe some peculiar solutions like flows in thin structures and motion of falling bodies.