It is a fundamental problem in representation theory to classify the finitely generated modules for a given finite dimensional algebra over a field. One approach to this problem is to give conditions for one module to be "simpler" than another in some sense. For example, because of the Jordan-H"older Theorem, one can take the semi-simplification of a module. In this talk I will introduce several partial orders that can be put on the isomorphism classes of finitely generated modules. I will then concentrate on one particular partial order coming from taking closures of orbits under the action of an algebraic group. I will discuss two different settings in which this occurs, one affine and the other projective. At the end I will raise some questions and give some answers in a low-dimensional setting.