We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from \(L^\infty ({\mathbb {B}})\) to \({\mathcal {B}}\) , and from \(C_0({\mathbb {B}})\) to \({\mathcal {B}}_0\) are onto. We verify that the dual space of the hyperbolic harmonic Bergman space \({\mathcal {B}}^1_\alpha \) is \({\mathcal {B}}\) and its predual is \({\mathcal {B}}_0\) . Finally, we obtain atomic decompositions of Bloch functions as series of Bergman reproducing kernels.
