Abstract: A Hermitian metric on a complex manifold is called balanced if its fundamental form is co-closed. In the talk I will review some general results about balanced metrics and the Hull-Strominger system. In particular, I will show that the Fu-Yau solution to this system on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. This is a joint work with G. Grantcharov and L. Vezzoni.