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