  Summarizing the results of arXiv:0707.1038, we discuss the four-dimensional
effective approach to type II N=1 supersymmetric flux compactifications with
general SU(3)x SU(3)-structure. In particular, we study the effect of a
non-trivial warp factor, which we argue leads naturally to a supergravity
formulation invariant under local complexified Weyl transformations. We show
that the full ten-dimensional supersymmetry equations can be obtained as
F-flatness and D-flatness conditions from the superpotential and Kaehler
potential. We then consider non-perturbative corrections to these supersymmetry
conditions, following from adding instanton or gaugino condensation effects to
the superpotential. As examples, we show how smeared instantons allow to
understand the ten-dimensional geometry of KKLT-like AdS vacua and we give an
explanation for the superpotential for "mobile" D3-branes in terms of a
non-perturbatively induced generalized complex structure.
