Arithmetic manifolds are hyperbolic manifolds constructed from number theoretic data. By their very definition, they exhibit a strong connection between algebraic invariants, such as trace fields, and geometric quantities like lengths of closed geodesics. Despite this, the geometry of these manifolds remains surprisingly mysterious. Nevertheless, a guiding philosophy is that arithmetic manifolds should be the most symmetric hyperbolic manifolds and therefore exhibit geometric phenomena that are rare or absent in generic hyperbolic manifolds. In this talk, I will survey arithmetic hyperbolic manifolds, likely focusing on low dimensions, and discuss several manifestations of this philosophy, both known and conjectural. I will then discuss new work furthering this philosophy by establishing finiteness of closed arithmetic surface bundles, resolving a conjecture of Bowditch, Maclachlan, and Reid.