This chapter develops the theoretical framework. It defines international orders as configurations of authority. It then conceptualizes representants as effectively integrating material and ideational features, while being irreducible to either. It explains how representants relate to discourses, and material resources, and highlights the value-added of representants in relation to cognate concepts, like Bourdieu’s symbolic capital, status symbols, or Pitkin’s representation. Representants do not come alone, but are embedded into semeiotic webs. On this basis the chapter develops four mechanisms through which representants constitute international orders: they characterize the units of international politics, they legitimize them, they position them in power relations towards each other, and they serve as tools for governing. Representants are constitutive of international orders, while also being the building blocks political agents use to change orders. The chapter develops two mechanisms of changes in representants. One focuses on struggles between actors over getting specific representants socially recognized. The other is an unintentional change in representants themselves. It outlines why some artifacts, practices, and language become socially recognised representants. The last section develops a semeiotics of materialism to study representants and capture the constitutive effects of material reality on a par with those of language.