Motivated by operator systems, we discuss ordered vector spaces with order units. We will first describe what happens in the real setting, and talk about the difficulty involved in forming quotients of Archimedean ordered spaces. We will then talk about complex vector spaces and discuss how a theory of ordered *-vector spaces may be developed. In the complex setting, we will see that the situation is more ramified, and in particular a number of different norms must be considered to understand the theory.