Relativistic electrons emit synchrotron radiation due to their gyro- and guiding-center motions in a curved magneticeld. In this paper, 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, thedynamics of runaway electrons is examined and a steady-state solution is constructed describing a balance between acceleration by the electriceld, pitch-angle scattering,and radiation reaction. Furthermore, it is found that a beam of relativistic electrons can be slowed down by the combined eects 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)