  We investigate the orbifold limits of string theory compactifications with
geometric and non-geometric fluxes. Exploiting the connection between internal
fluxes and structure constants of the gaugings in the reduced supergravity
theory, we can identify the types of fluxes arising in certain classes of
freely-acting symmetric and asymmetric orbifolds. We give a general procedure
for deriving the gauge algebra of the effective gauged supergravity using the
exact CFT description at the orbifold point. We find that the asymmetry is, in
general, related to the presence of non-geometric Q- and R- fluxes. The action
of T-duality is studied explicitly on various orbifold models and the resulting
transformation of the fluxes is derived. Several explicit examples are
provided, including compactifications with geometric fluxes, Q-backgrounds
(T-folds) and R-backgrounds. In particular, we present an asymmetric Z4xZ2
orbifold in which all geometric and non-geometric fluxes {\omega}, H, Q, R are
turned on simultaneously. We also derive the corresponding flux backgrounds,
which are not in general T-dual to geometric ones, and may even simultaneously
depend non-trivially on both the coordinates and their winding T-duals.
