The behavior of electromagnetic processes in strong magnetic fields is currently of great interest in high-energy astrophysics. Observations of neutron stars indicate that magnetic fields larger than 1012Gauss exist in nature. In fields this strong, where electrons behave much as if they were in bound atomic states, familiar processes undergo profound changes and exotic processes become important. Strong magnetic fields affect the physics in several fundamental ways: energies prependicular to the field are quantized, transverse momentum is not conserved and electron/positron spin is important. The relaxation of transverse mometum conservation allows first order processes and their inverses: one-photon pair production and annihilation, synchrotron/cyclotron radiation and absorption, which are kinematically forbidden under field-free conditions. The first two are essentially quantum-mechanical and hence significant only in fields whose strength approaches the critical field,Bcr= 4.414 × 1013Gauss. One-photon pair production is likely to be the dominant source ofe+-e−pairs in fields exceeding 1012Gauss. While synchrotron radiation and absorption are observable as classical electromagnetic processes in weak fields, they are considerably different in high fields, where the classical synchrotron radiation formulae can violate conservation of energy, and predict too large an emissivity and electron energy loss rate. The second-order processes: two-photon pair production and annihilation and Compton Scattering, are also modified in strong fields. The discreteness ofe+- e−pair states causes resonant behavior in the cross sections and decreases the second-order rates from their free-space values. These processes play an important role in modelling high energy emission from pulsars and gamma-ray bursts.