The exterior limit of a Black Hole is considered by studying
the related concept, introduced by Penrose on the 1960's, of a closed
trapped surface. The physical meaning of these surfaces and their
relevance will be briefly analyzed. Some surprising non-local
properties will be presented. The natural candidates for the surface
of a Black Hole, its event horizon or trapping horizons, have some
problems: the former suffers from a global teleological problem,
the latter will be seen to be crossed by closed trapped surfaces.
Thus, the question of how to define the surface of a black hole
may be related with the exterior boundary enclosing all closed
trapped surfaces. Some examples will be given.
