  Various approaches to T-duality with NSNS three-form flux are reconciled.
Non-commutative torus fibrations are shown to be the open-string version of
T-folds. The non-geometric T-dual of a three-torus with uniform flux is
embedded into a generalized complex six-torus, and the non-geometry is probed
by D0-branes regarded as generalized complex submanifolds. The
non-commutativity scale, which is present in these compactifications, is given
by a holomorphic Poisson bivector that also encodes the variation of the
dimension of the world-volume of D-branes under monodromy. This bivector is
shown to exist in SU(3) x SU(3) structure compactifications, which have been
proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors
are generically not parallel, thereby giving rise to a non-trivial Poisson
bivector. Furthermore we show that for non-geometric T-duals, the Poisson
bivector may not be decomposable into the tensor product of vectors.
