When is an operator system a C*-algebra?

In the category of operator systems, identification comes via complete order isomorphisms, and so an operator system can be identified with a C*-algebra without itself being an algebra. So, when is an operator system a C*-algebra? This question has floated around the community for some time. From Choi and Effros, we know that injectivity is sufficient, but certainly not necessary outside of the finite-dimensional setting. In this talk, I will give a characterization in the separable nuclear setting coming from C*-encoding systems. This comes from joint work with Galke, van Lujik, and Stottmeister.