I will present recent work towards establishing a duality on regular tilings of hyperbolic space. Discrete holography is of interest to a broad audience reaching - beyond holographers - from mathematiciants interested in CFTs on fractals to condensed matter scientists and electrical engineers studying hyperbolic lattices. In the talk, I will present a recent example where an aperiodic XXZ spin chain is obtained naturally by extrapolating the bulk AdS2 tiling to its boundary. The properties of this model are studied using RG techniques, which provide a tensor network construction for its ground state. We calculate and compare the entanglement entropy and mutual information both at the boundary and in the bulk. I wil describe how to use matrix models towards obtaining a full duality for discrete systems.