Given a minimal dynamical system on a compact metric space one may construct a C*-algebra which is in a certain sense equivalent to the algebra of continuous functions on the orbit space. Since the resulting C*-algebra is simple, separable, unital and nuclear, we can calculate its so-called Elliott invariant (roughly, K-theory and tracial states). Orbit equivalent systems will always yield the same invariant, so we can also see this as an invariant for the dynamical systems themselves. If we restrict to minimal dynamical systems with mean dimension zero, then this invariant is able to distinguish the corresponding C*-algebras up to *-isomorphism. It is known what the range of the Elliott invariant is for simple separable unital nuclear C*-algebras, but we still do not know the range for the class of C*-algebras which arise from minimal dynamical systems. In my talk I will discuss what is known about the titular question, as well as what we might require for a complete answer.