We develop the representation of bulk operators in AdS as smeared operators on the complexified boundary. We treat general AdS in Poincare coordinates and AdS_3 in Rindler coordinates. This enables us to represent bulk operators inside the horizon of a BTZ black hole. We verify that these operators give the correct bulk two point functions, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and the reduction in the number of degrees of freedom at finite N.