non-unital operator systems are norm closed subspaces of b(h) that are closed under the involution map $x \mapsto x^*$. for example, c*-algebras are examples of non-unital operator systems. much like gelfand duality, a result of kadison from the 80s shows that operator systems generated by commuting elements are categorically dual to a class of geometric structures, namely compact convex sets. unlike the c*-theory, a remarkable result due to webster-winkler and davidson-kennedy shows that kadison's duality theorem readily generalizes to the non-commutative unital setting as well. in our talk, we discuss kadison’s original duality as well as the nc convex duality for non-commutative operator systems due to myself, matt kennedy, and nick manor. finally, we will have a discussion of some results on the side of operator systems that this illuminates.