Two layers of magnetic materials separated by a nonmagnetic ''spacer''
layer display an exchange coupling between the separated magnetic lay
ers, as detailed by the papers on experimental aspects of magnetic mul
tilayers in this issue. Here we describe from a personal perspective t
he current theoretical understanding of exchange coupling in magnetic
multilayers. The understanding by this point is quite good, and involv
es contributions from a number of authors, of which we review a key su
bset. The organization of the paper is as follows. After an introducti
on to RKKY coupling, the next section discusses the effects of a reali
stic band structure (with emphasis on the work of Herman et al., Bruno
and Chappert, and Stiles). The following section, which introduces qu
antum wells, covers the work of Mathon et al., Bruno et al., and this
author. Finally, we include a discussion of the predictability of ampl
itude, period, and phase, including the effects of disorder.