  This survey starts with the historical landmarks leading to the study of
principal configurations on surfaces, their structural stability and further
generalizations. Here it is pointed out that in the work of Monge, 1796, are
found elements of the qualitative theory of differential equations (QTDE),
founded by Poincar\'e in 1881. Here are also outlined a number of recent
results developed after the assimilation into the subject of concepts and
problems from the QTDE and Dynamical Systems, such as Structural Stability,
Bifurcations and Genericity, among others, as well as extensions to higher
dimensions. References to original works are given and open problems are
proposed at the end of some sections.
