Recent observations of soft gamma-ray repeaters and anomalous X-ray pulsars are furnishing greater evidence for the existence of a class of neutron stars with surface magnetic fields exceeding the critical field of4.4×1013&hthinsp;Gauss.The main effort of this study is to understand the role of relativistic Compton scattering as it operates with other QED processes, to develop approximate expressions of the exact rate and to incorporate them in a full acceleration-cascade model. Previous modeling of Compton scattering in magnetic fields has assumed that the scattering cross section can be adequately described by the nonrelativistic Compton scattering cross section (Thomson limit) below resonance and at the resonance, and the Klein-Nishina cross section above the resonance. Consequently, these studies have not included the effects of the strong fields of pulsars and magnetars. The study of the strong field effects on the inverse Compton scattering process will provide insight into the particle-photon interactions associated with a variety of pulsar phenomena, burst spectra of soft gamma-ray repeaters and the transport of thermal radiation through neutron star atmospheres. This paper will summarize the role of inverse Compton scattering and the effects of strong magnetic fields upon the integrated cross section for Compton scattering. An analytical approximation to the exact QED cross section will be discussed. ©2000 American Institute of Physics.