We will discuss a new characterization of an important class of objects known as W*-modules, also called selfdual Hilbert C^*-modules over a von Neumann algebra. We describe how this leads to a generalization of the theory of W*-modules to the setting of non-selfadjoint algebras of Hilbert space operators which are closed in the weak*-topology. We also discuss how the earlier theory of rigged modules due to Blecher, transfers to the weak*-topology setting.