We review various aspects of compactifications of heterotic and type II supergravities on six dimensional manifolds. In the general framework of non-K?hler compactifications, emphasis is made on a particular class of manifolds with SU(3)-structure named half-flat. We recall how these manifolds appeared in the context of mirror symmetry of type II theories, providing mirror configurations to Calabi-Yau compactifications with NS-NS electric fluxes. In the heterotic sector, they generate a potential for all moduli, and are expected to break the E8 × E8 gauge group down to SO(10) × E8 in 4 dimensions.
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