  The stability of black holes and solitons in d-dimensional Anti-de Sitter
space-time against scalar field condensation is discussed. The resulting
solutions are "hairy" black holes and solitons, respectively. In particular, we
will discuss static black hole solutions with hyperbolic, flat and spherical
horizon topology and emphasize that two different type of instabilities exist
depending on whether the scalar field is charged or uncharged, respectively. We
will also discuss the influence of Gauss-Bonnet curvature terms. The results
have applications within the AdS/CFT correspondence and describe e.g.
holographic insulator/conductor/superconductor phase transitions.
