  The concept of closed trapped surface is of paramount importance in General
Relativity and other gravitational theories. However, it is a purely
geometrical object. With the aim of bringing this concept to closer attention
by the mathematical community, I introduce the generalized idea of trapped
submanifold by using the causal character of the mean curvature vector. Trapped
surfaces can thus be easily seen to be generalizations, possible in
semi-Riemannian geometry, of the standard concepts of minimal surfaces, maximal
hypersurfaces, geodesics, and the like. Selected applications are mentioned.
