An orientable hyperbolic n-manifold is isometric to the quotient of hyper-
bolic n-space H by a discrete torsion free subgroup of the group of
orientation-preserving isometries of H. Among these manifolds, the ones
originating from arithmetically defined groups form a family of special
interest. Due to the underlying connections with number theory and the
theory of automorphic forms, there is a fruitful interaction between
geometric and arithmetic questions, methods and results. We intend to give
an account of recent investigations in this area, in particular, of those
pertaining to hyperbolic 3-manifolds and bounds for their Betti numbers.
