An outline classification is given of the Heterostraci, with diagnoses of the following orders and suborders:  Astraspidiformes, Eriptychiiformes, Cyathaspidiformes (Cyathaspidida, Poraspidida, Ctenaspidida), Psammosteiformes (Tesseraspidida, Psarnmosteida), Traquairaspidiformes, Pteraspidiformes (Pteraspidida, Doryaspidida), Cardipeltiformes and Amphiaspidiformes (Amphiaspidida, Hibernaspidida, Eglonaspidida). It is shown that the various orders fall into four main evolutionary lineages - cyathaspid, psammosteid, pteraspid and amphiaspid, and these are traced from primitive tessellated forms. A tentative phylogeny is proposed and alternatives are discussed.