The classical low-dimensional models of thin structures are based on certain
a priori assumptions on the three-dimensional deformation and/or stress fields,
diverse in nature but all motivated by the smallness of certain dimensions with
respect to others. In recent years, a considerable amount of work has been done
in order to rigorously justify these a priori assumptions; in particular,
several techniques have been introduced to make dimension re- duction rigorous.
We here review, and to some extent reformulate, the main ideas common to these
techniques, using some explicit dimension-reduction problems to exemplify the
points we want to make.