  We describe a simple and yet surprisingly powerful probabilistic technique
which shows how to find in a dense graph a large subset of vertices in which
all (or almost all) small subsets have many common neighbors. Recently this
technique has had several striking applications to Extremal Graph Theory,
Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this
survey we discuss some of them.

Combinatorics;Probability