We study the leading and next-to-leading eikonal phase in the context of AdS/CFT. In the bulk side, we compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. The leading eikonal phase shift in 4d holographic CFTs can be computed using conformal Regge theory while the computation of the next-to-leading order eikonal phase shift relies on a new universal formula for the lowest-twist OPE of double-trace stress-tensors with two scalar operators. These OPE coefficients are consistent with the second-order phase shift as well as anomalous dimensions obtained in AdS black holes in the lightcone limit. In relations to the idea of “eikonalization” of the stress-tensor sector in holographic CFTs, we comment on hints of a structure similar to the vacuum Virasoro block in 2d CFT.