  We undertake a systematic analysis of non-geometric backgrounds in string
theory by seeking stringy liftings of a class of gauged supergravity theories.
In addition to conventional flux compactifications and non-geometric T-folds
with T-duality transition functions, we find a new class of non-geometric
backgrounds with non-trivial dependence on the dual coordinates that are
conjugate to the string winding number. We argue that T-duality acts in our
class of theories, including those cases without isometries in which the
conventional Buscher rules cannot be applied, and that these generalised
T-dualities can take T-folds or flux compactifications on twisted tori to
examples of the new non-geometric backgrounds. We show that the new class of
non-geometric backgrounds and the generalised T-dualities arise naturally in
string field theory, and are readily formulated in terms of a doubled geometry,
related to generalised geometry. At special points in moduli space, some of the
non-geometric constructions become equivalent to asymmetric orbifolds which are
known to provide consistent string backgrounds. We construct the bosonic sector
of the corresponding gauged supergravity theories and show that they have a
universal form in any dimension, and in particular construct the scalar
potential. We apply this to the supersymmetric WZW model, giving the complete
non-linear structure for a class of WZW-model deformations.
