  Using elementary rigorous methods we prove the existence of a clustered phase
in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are
grouped into clusters which are far away from each other. The results are in
agreement with previous predictions of the cavity method and give a rigorous
confirmation to one of its main building blocks. It can be generalized to other
systems of both physical and computational interest.
