 The Ising Exchange interaction is a limiting case of strong exchange anisotropy and represents a key property of many magnetic materials, with necessary and sufficient conditions established for metal sites with unquenched orbital moments. It can be of two types, coaxial or non-coaxial, with magnetic moments directed along the anisotropy axes on the metal sites or with arbitrary orientation of one of the magnetic moments. These findings will contribute to purposeful design of lanthanide and actonide-based materials. This article was authored by Leavu F. Chibotaru and Naoya Iwahara.