Conduction and valence band edges in diluted magnetic semiconductors u
ndergo enormous Zeeman shifts when a magnetic field is applied, reachi
ng values in excess of 100 meV at low temperatures. These Zeeman shift
s can thus have profound consequences on the properties of DMS/non-DMS
heterostructures, since they provide the opportunity of tuning their
band alignment by varying an applied field. This leads to a variety of
entirely new effects, and also provides a powerful tool for probing t
he effect of band alignment on the properties of semiconductor heteros
tructures in general. We illustrate this with several examples. First,
using the ZnSe/ZnMnSe system, we discuss the creation of a spatial sp
in modulation (spin superlattice). Second, we use the drastic differen
ces in the Zeeman splitting occurring in different layers of a DMS/non
-DMS superlattice in order to pinpoint the localization in space of th
e specific electronic states involved in optical transitions. We illus
trate this by investigating the localization of above-barrier states i
n type-I ZnSe/ZnMnSe superlattices, and of spatially-direct (type-I) e
xcitons which occur in ZnTe/CdMnSe and ZnMnTe/CdSe type-II superlattic
es. Finally, we exploit Zeeman tuning to demonstrate the confinement e
ffects which occur in a single quantum barrier.