  We propose and explore the Regge limit for correlation functions of five
local primary operators in conformal field theories. After reviewing some
features of Regge theory for flat-space scattering amplitudes, we analyse the
analytic structure of conformal blocks both in position and Mellin space in the
Regge limit and propose an extension of conformal Regge theory for five-point
functions. As a byproduct of our analysis we also introduce a new basis of
three-point correlation functions for operators with spin and the associated
Euclidean conformal blocks.
