  We review several results related to the characterization of polyhedra in
hyperbolic 3-space. In particular we present Rivin's theorem that gives a
characterization of compact convex hyperbolic polyhedra, and Hodgson's proof of
the Adreev's theorem. We also review the analogous characterization of ideal
polyhedra, and give a family of counter-examples that proves that hyperbolic
polyhedra are not determined by edge lengths.
