Correlators in field theories at finite temperatures have singularities on the light cone. Are there any other singularities? In this talk, I will address this question in the context of holographic theories in the black hole phase. Two points on the AdS boundary can be connected by a null geodesic in the bulk, leading to a so-called bulk-cone singularity. These new singularities were previously conjectured by analyzing the geodesic approximation, but we will derive them in full generality by developing the technology of thermal Regge theory. The functional form of the singularity leads to sharp signatures of the AdS photon sphere in the boundary CFT, including an identification of the boundary dual of the angular velocity and Lyapunov exponent associated with the photon sphere. I will also comment on the resolution of the singularity by stringy effects.