  The SNe type Ia data admit that the Universe today may be dominated by some
exotic matter with negative pressure violating all energy conditions. Such
exotic matter is called {\it phantom matter} due to the anomalies connected
with violation of the energy conditions. If a phantom matter dominates the
matter content of the universe, it can develop a singularity in a finite future
proper time. Here we show that, under certain conditions, the evolution of
perturbations of this matter may lead to avoidance of this future singularity
(the Big Rip). At the same time, we show that local concentrations of a phantom
field may form, among other regular configurations, black holes with
asymptotically flat static regions, separated by an event horizon from an
expanding, singularity-free, asymptotically de Sitter universe.
