We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in N=4 Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the 't Hooft coupling the behaviour near J=1 of the OPE coefficients C_{OOJ} between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory - in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient C_{LLJ} between two Lagrangians and the leading twist operators of spin J.

We derive the eikonal approximation to high energy interactions in Anti-de Sitter spacetime, resuming in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual CFT four point function for small values of cross ratios, in a Lorentzian regime. We explore the consequences of this result to the dual CFT. In the planar limit this Lorentzian amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling. At large coupling, the pole corresponds to graviton exchange in AdS, whereas at weak coupling, the pole is that of the hard perturbative BFKL pomeron. The conformal symmetry of the transverse space E2 is trivially realized on the dual holographic space H3, allowing for a unified description of both weak and strong 't Hooft coupling regimes. The analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation.