Abstract
In this paper I aim to review work on simple Ising models, the axial Ising models, which provide a useful phenomenological representation of modulated order in many compounds. The prototype of these systems is the axial next nearest neighbor Ising or ANNNI model and the first part of the article is devoted to a description of its phase diagram with emphasis on the features which might be observed experimentally. I then discuss the extent to which this behavior is in fact seen in polytypes, binary alloys and a ferrimagnet, cerium antimonide.
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