  We describe all supersymmetric solutions of the heterotic string which
preserve 8 supersymmetries and show that are distinguished by the holonomy,
${\rm hol}(\hat\nabla)$, of the connection, $\hat\nabla$, with skew-symmetric
torsion. The ${\rm hol}(\hat\nabla) \subseteq SU(2)$ solutions are principal
bundles over a 4-dimensional hyper-K\"ahler manifold equipped with a
anti-self-dual connection and fibre group $G$ which has Lie algebra,
${\mathfrak Lie} (G)=\bR^{5,1}$, $\mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)$
or $\mathfrak{cw}_6$. Some of the solutions have the interpretation as 5-branes
wrapped on $G$ with transverse space any hyper-K\"ahler 4-dimensional manifold.
We construct new solutions for ${\mathfrak Lie} (G)=\mathfrak{sl}(2,\bR)\oplus
\mathfrak{su}(2)$ and show that are characterized by 3 integers and have
continuous moduli. There is also a smooth family in this class with one
asymptotic region and the dilaton is bounded everywhere on the spacetime. We
also demonstrate that the worldvolume theory of the backgrounds with holonomy
SU(2) can be understood in terms of gauged WZW models for which the gauge
fields are composite. The ${\rm hol}(\hat\nabla) \subseteq\bR^8$ solutions are
superpositions of fundamental strings and pp-waves in flat space, which may
also include a null rotation. The ${\rm hol}(\hat\nabla)=\{1\}$ heterotic
string backgrounds which preserve 8 supersymmetries are Lorentzian group
manifolds.
