Resonant X-ray scattering has been observed in lanthanides and actinides. The observed scattering is sensitive to magnetization, but it arises primarily from electric, rather than magnetic, multipole transitions. The magnetic sensitivity is due to "exchange" effects and to spin-orbit correlations in one or both of the levels involved in the resonance. "Exchange" effects include the exclusion principle, which permits transitions only to vacant orbitals in partially filled shells, and exchange splitting in band states. The elastic scattering amplitude contains terms dependent on the direction of the magnetic moment up to quadratic order for E1 transitions and up to quartic order for E2 transitions. In coherent scattering of X-rays from spiral antiferromagnets, the magnetic sensitivity results in the formation of resonant magnetic satellites associated with the Bragg peaks. This effect provides a new type of probe for the investigation of magnetic structures.