Abstract: Balanced HKT metrics in hypercomplex geometry are thought to be the quaternionic analog of Calabi-Yau metrics in Kahler geometry. In this talk, first we prove the openness of balanced HKT cone inside the cone of HKT structures on a compact hypercomplex manifold. We also study the Lie algebra of hyperholomorphic vector fields. For instance, we prove a harmonicity property for forms dual to hyperholomorphic vector fields. This is joint work with Giovanni Gentili.