  We study Anderson localization in disordered tight-binding models on
hyperbolic lattices. Such lattices are geometries intermediate between ordinary
two-dimensional crystalline lattices, which localize at infinitesimal disorder,
and Bethe lattices, which localize at strong disorder. Using state-of-the-art
computational group theory methods to create large systems, we approximate the
thermodynamic limit through appropriate periodic boundary conditions and
numerically demonstrate the existence of an Anderson localization transition on
the $\{8,3\}$ and $\{8,8\}$ lattices. We find unusually large critical disorder
strengths, determine critical exponents, and observe a strong finite-size
effect in the level statistics.
