Given a pair of unital subspaces V and W inside B(H), one can form another unital sub- space by considering the linear span of all products of the form vw where v is an element of V and w is an element of W. In this talk, we will abstractly characterize unital subspaces which arise in this way. We will also consider important "abstract" examples of products of unital operator spaces, including the Haagerup tensor product and the commuting tensor product. This talk is based on ongoing joint work with Adam Dor-On.