We develop an approach to the high-energy limit of gauge theories based on the universal properties of their infrared singularities. Our main tool is the dipole formula, a compact ansatz for the all-order infrared singularity structure of scattering amplitudes of massless partons. By taking the high-energy limit, we show that the dipole formula implies Reggeization of infrared-singular contributions to the amplitude, at leading logarithmic accuracy, for the exchange of arbitrary color representations in the cross channel. We observe that the real part of the amplitude Reggeizes also at next-to-leading logarithmic order, and we compute the singular part of the two-loop Regge trajectory, which is universally expressed in terms of the cusp anomalous dimension. Our approach provides tools to study the high-energy limit beyond the boundaries of Regge factorization: thus we show that Reggeization generically breaks down at next-to-next-to-leading logarithmic accuracy, and provide a general expression for the leading Reggeization-breaking operator. Our approach applies to multiparticle amplitudes in multi-Regge kinematics, and it also implies new constraints on possible corrections to the dipole formula, based on the Regge limit.