Relativistic electrons emit synchrotron radiation due to their gyro- and guiding-center motions in a curved magnetic field. In this article, the kinetic theory of relativistic electron beams is developed to account for radiation reaction by including the Abraham–Lorentz reaction force in the kinetic equation. As an application of this theory, the dynamics of runaway electrons is examined and a steady-state solution is constructed describing a balance between acceleration by the electric field, pitch-angle scattering, and radiation reaction. Furthermore, it is found that a beam of relativistic electrons can be slowed down by the combined effects of pitch-angle scattering and radiation reaction. This damping can be more efficient than ordinary collisional drag, and appears to explain the decay of post-disruption runaway currents in the Joint European Torus (JET) [R. D. Gill, Nucl. Fusion 33 , 1613 (1993)].