We will describe black holes in AdS with hyperbolic horizons, and obtain a holographic description of the region inside the horizon, focusing on the dynamics of the scalar fields in the dual gauge theory. This leads to a proposal for a dual description of D-branes falling through the horizon of any AdS black hole. The proposal uses a field-dependent time reparameterization in the field theory. We relate this reparametrization to various gauge invariances of the theory. Finally, we speculate on information loss and the black hole singularity in this context. This talk will be based on arxiv:0904.3922, and ongoing work with the same authors.