Many structures consisting of magnetic layers separated by a nonmagnetic spacer layer show an oscillatory exchange coupling. This behavior is explained in terms of a simple model that shows that the Fermi surface of the spacer-layer material is responsible for the oscillatory coupling. The periods of the oscillatory coupling are set by extremal spanning vectors of the Fermi surface of the spacer-layer material. The strength of the coupling depends both on the geometry of the Fermi surface and on the reflection amplitudes for electrons scattering from the interfaces between the spacer layers and the magnetic layers. To test this and related models, the extremal spanning vectors and the associated Fermi-surface geometrical factors have been calculated for a large set of spacer-layer materials and interface orientations. These models are at least consistent with the experimental data. All measured oscillation periods are consistent with the calculated periods, but particularly for transition metals there are many more periods calculated than are seen experimentally.