In this talk, I will report on the works that I did with Jun Li and Fu
on constructing Non-Kahler complex manifolds that can be used as a supersymmetric string vacuum solution.
The equations were proposed by Strominger twenty years ago. They admit parallel spinors and support a balanced metric. 
In our work, we give the first smooth solution of these Strominger equations.
It couples stable bundle with hermitian metrics on the manifold. We believe that the solution would give contribution to understanding important non-Kahler manifolds that are constructed in a natural manner, such as the construction of Clemens on Calabi-Yau manifolds.