In 2008, J.X. Fu and S.T. Yau introduced a new fully nonlinear PDE on compact complex manifolds. The equation arises as a reduction of the Hull-Strominger system of theoretical physics in the special case of certain non-Kahler torus fibrations over a Calabi-Yau manifold. We will discuss recent developments in the study of this equation and its generalization to a family of fully nonlinear PDE without concave second order terms. This is joint work with D.H. Phong and X.-W. Zhang.