  We study the topological sector of N=2 sigma-models with H-flux. It has been
known for a long time that the target-space geometry of these theories is not
Kahler and can be described in terms of a pair of complex structures, which do
not commute, in general, and are parallel with respect to two different
connections with torsion. Recently an alternative description of this geometry
was found, which involves a pair of commuting twisted generalized complex
structures on the target space. In this paper we define and study the analogues
of A and B-models for N=2 sigma-models with H-flux and show that the results
are naturally expressed in the language of twisted generalized complex
geometry. For example, the space of topological observables is given by the
cohomology of a Lie algebroid associated to one of the two twisted generalized
complex structures. We determine the topological scalar product, which endows
the algebra of observables with the structure of a Frobenius algebra. We also
discuss mirror symmetry for twisted generalized Calabi-Yau manifolds.
