In recent years there is a growing interest in unconventional string backgrounds with non-geometric fluxes. The latter often appear after repeated T-dualities on known backgrounds. However, a very interesting question regards whether these fluxes can coexist in generalized geometries without a geometric dual. In this talk we address this question and we show that in principle there exist such geometries where all types of fluxes coexist. Our strategy consists in using generalized geometry and in particular Dirac structures, which are subbundles of the generalized tangent bundle where the Courant bracket is associative and field strengths transform tensorially. We study the mathematical description of fluxes on Dirac structures and then combine the latter into Courant algebroids that describe multi-flux geometries. Furthermore we discuss the sources of non-geometric fluxes, which are heavy extended objects known as exotic branes. These branes exhibit a wide range of world volume dimensions, tension scalings and monodromy properties, and we argue that they couple to certain mixed symmetry tensors, which are exotic magnetic duals of the supergravity background fields.