In this talk we discuss the geometric and non-geometric faces of closed string vacua arising by T-duality from torus bundles with constant H-flux. The associated closed string geometries are described by new non-commutative as well as non-associative algebras, which can be characterized by certain 3-cocycles in Lie algebra cohomology. We present a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization.