Experiments and subsequent theoretical studies on the integer and fractional quantum anomalous Hall effects in few-layer graphene structures recently lead to the prediction of anomalous Hall crystals (AHCs), a phase in which strong interactions drive electrons to spontaneously crystallize, forming an insulator with a non-trivial Chern number. I will first briefly review the experiments that lead to this prediction and the toy models that have been developed to study AHCs. I will then move on to discussing our work theoretically characterizing anomalous Hall crystals. We first consider the elastic properties of AHCs, finding that their non-trivial topology limits the stiffness of the crystal, and that accounting for the non-parabolic dispersion of RNG can drive a mechanical instability. Motivated by the relation between mechanical properties and phonons, we compute the Chern numbers of phonons and excitons in AHCs using time-dependent Hartree-Fock, finding that they are themselves often topological. Finally, I will conclude by discussing the experimental implications of topological phonons.