Enterprise architecture is concerned with the fundamental organization of the operating environment of an enterprise. The enterprise architecture is used to plan and control the construction of the systems that populate the operating environment. As the scope covered can be considerable in large enterprises, introducing domain architectures to partition and detail the enterprise architecture is a plausible approach. We formulate prescriptive criteria that consistent domain architectures must meet. By integrating the creation of domain architectures into an extended strategic alignment model we develop a theory that accounts for both the creation, scope-setting and detailing. Based on the creation viewpoint we derive a multi-level classification taxonomy. The primary differentiator is that between domains that are created from business usage viewpoints and those that are created from solution construction viewpoints. Four cases of domain architectures from actual practice are described that illustrate the variety encountered. Domain classifications in all cases conform to the theoretical model. The criteria, the developed theory and the cases have both academic relevance as well as significance for practitioners.