  Using F-theory/heterotic duality, we describe a framework for analyzing
non-geometric T2-fibered heterotic compactifications to six- and
four-dimensions. Our results suggest that among T2-fibered heterotic string
vacua, the non-geometric compactifications are just as typical as the geometric
ones. We also construct four-dimensional solutions which have novel type IIB
and M-theory dual descriptions. These duals are non-geometric with three- and
four-form fluxes not of (2,1) or (2,2) Hodge type, respectively, and yet
preserve at least N=1 supersymmetry.
