Although IIA and IIB are dual descriptions of the same underlying theory, the ensembles of flux compactifications in each theory appear markedly different. Studying the action of T-duality on flux compactifications suggests that one may need to introduce new discrete parameters, corresponding to generalized or nongeometric fluxes, in order to describe solutions of the full theory. I will illustrate these ideas in the context of a simple toroidal model and describe the features of the resulting compactifications.