Abstract: Using the rings of Lipschitz and Hurwitz integers in the quaternion division algebra of the quaternions we define several Kleinian discrete subgroups of isometries of hyperbolic 4-space. These groups are a quaternionic versions of the classical modular group and Picard group. The quotients of hyperbolic 4-space by the action of these groups give examples of arithmetic orbifolds which are finitely covered by very interesting arithmetic hyperbolic 4-manifolds of finite volume.