  The spinorial geometry method of solving Killing spinor equations is reviewed
as it applies to 6-dimensional (1,0) supergravity. In particular, it is
explained how the method is used to identify both the fractions of
supersymmetry preserved by and the geometry of all supersymmetric backgrounds.
Then two applications are described to systems that exhibit superconformal
symmetry. The first is the proof that some 6-dimensional black hole horizons
are locally isometric to $AdS_3\times \Sigma^3$, where $\Sigma^3$ is
diffeomeorphic to $S^3$. The second one is a description of all supersymmetric
solutions of 6-dimensional (1,0) superconformal theories and in particular of
their brane solitons.
