Abstract: We review some recent progress in heterotic moduli
stabilization. In particular, it was recently shown that the heterotic
Bianchi Identity can be accounted for by the construction of a holomorphic
operator, which mathematically corresponds to a holomorphic double
extension. Moduli can then be computed in terms of cohomologies of this
operator. We will see how the same structure can be derived form a
Gukov-Vafa-Witten type superpotential. We also cover some examples, and
briefly consider obstructions and Yukawa couplings arising from these
structures.

Based on: 1402.1725, 1409.3347, 1411.6696, 1405.xxxxx