In this talk we will show how the Ramanujan complexes lead to solution of the geometric, and then the topological, Gromov overlapping problem. The technical tool is via the notion of ``coboundary expansion". This cohomological concept was developed parallelly and independently by Gromov for overlapping problems and by Linial-Meshulam in order to extend Erdős-Rényi theory of random graphs to higher dimensional simplicial complexes.