  We first recall several historical oscillating bridges that, in some cases,
led to collapses. Some of them are quite recent and show that, nowadays,
oscillations in suspension bridges are not yet well understood. Next, we survey
some attempts to model bridges with differential equations. Although these
equations arise from quite different scientific communities, they display some
common features. One of them, which we believe to be incorrect, is the
acceptance of the linear Hooke law in elasticity. This law should be used only
in presence of small deviations from equilibrium, a situation which does not
occur in strongly oscillating bridges. Then we discuss a couple of recent
models whose solutions exhibit self-excited oscillations, the phenomenon
visible in real bridges. This suggests a different point of view in modeling
equations and gives a strong hint how to modify the existing models in order to
obtain a reliable theory. The purpose of this paper is precisely to highlight
the necessity of revisiting classical models, to introduce reliable models, and
to indicate the steps we believe necessary to reach this target.
