  We discuss mirror symmetry in generalized Calabi-Yau compactifications of
type II string theories with background NS fluxes. Starting from type IIB
compactified on Calabi-Yau threefolds with NS three-form flux we show that the
mirror type IIA theory arises from a purely geometrical compactification on a
different class of six-manifolds. These mirror manifolds have SU(3) structure
and are termed half-flat; they are neither complex nor Ricci-flat and their
holonomy group is no longer SU(3). We show that type IIA appropriately
compactified on such manifolds gives the correct mirror-symmetric low-energy
effective action.
