  We review our present understanding of heterotic compactifications on
non-Kahler complex manifolds with torsion. Most of these manifolds can be
obtained by duality chasing a consistent F-theory compactification in the
presence of fluxes. We show that the duality map generically leads to
non-Kahler spaces on the heterotic side, although under some special conditions
we recover Kahler compactifications. The dynamics of the heterotic theory is
governed by a new superpotential and minimizing this superpotential reproduces
all the torsional constraints. This superpotential also fixes most of the
moduli, including the radial modulus. We discuss some new connections between
Kahler and non-Kahler compactifications, including some phenomenological
aspects of the latter compactifications.
