  Some selected applications of KT and HKT geometries in string theory,
supergravity, black hole moduli spaces and hermitian geometry are reviewed. It
is shown that the moduli spaces of a large class of five-dimensional
supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown
that a compact, conformally balanced, strong KT manifold whose associated KT
connection has holonomy contained in SU(n) is Calabi-Yau. The implication of
this result in the context of some string compactifications is explained.
