We investigate the orbifold limits of string theory compactifications withgeometric and non-geometric fluxes. Exploiting the connection between internalfluxes and structure constants of the gaugings in the reduced supergravitytheory, we can identify the types of fluxes arising in certain classes offreely-acting symmetric and asymmetric orbifolds. We give a general procedurefor deriving the gauge algebra of the effective gauged supergravity using theexact CFT description at the orbifold point. We find that the asymmetry is, ingeneral, related to the presence of non-geometric Q- and R- fluxes. The actionof T-duality is studied explicitly on various orbifold models and the resultingtransformation of the fluxes is derived. Several explicit examples areprovided, including compactifications with geometric fluxes, Q-backgrounds(T-folds) and R-backgrounds. In particular, we present an asymmetric Z4xZ2orbifold in which all geometric and non-geometric fluxes {\omega}, H, Q, R areturned on simultaneously. We also derive the corresponding flux backgrounds,which are not in general T-dual to geometric ones, and may even simultaneouslydepend non-trivially on both the coordinates and their winding T-duals.