  This review article consists of two parts. In the first part we use the
formalism of (exceptional) generalized geometry to derive the scalar field
space of SU(2)xSU(2)-structure compactifications. We show that in contrast to
SU(3)xSU(3) structures, there is no dynamical SU(2)xSU(2) structure
interpolating between an SU(2) structure and an identity structure.
Furthermore, we derive the scalar manifold of the low-energy effective action
for consistent Kaluza-Klein truncations as expected from N=4 supergravity.
  In the second part we then determine the general conditions for the existence
of stable Minkowski and AdS N=1 vacua in spontaneously broken gauged N=2
supergravities and construct the general solution under the assumption that two
appropriate commuting isometries exist in the hypermultiplet sector.
Furthermore, we derive the low-energy effective action below the scale of
partial supersymmetry breaking and show that it satisfies the constraints of
N=1 supergravity. We then apply the discussion to special quaternionic-Kahler
geometries which appear in the low-energy limit of SU(3)xSU(3)-structure
compactifications and construct Killing vectors with the right properties.
Finally we discuss the string theory realizations for these solutions.
