  The fundamental property of Fano varieties with mild singularities is that
they have a finite polyhedral Mori cone. Thus, it is very interesting to ask:
What we can say about algebraic varieties with a finite polyhedral Mori cone? I
give a review of known results.
  All of them were obtained applying methods which were originated in the
theory of discrete groups generated by reflections in hyperbolic spaces with a
fundamental chamber of finite volume.
  This is my report on Fano conference in Torino, October 2002
