In the paper ``Formal noncommutative symplectic geometryA'A', Maxim Kontsevich introduced three versions of cochain complexes GC_{Com}, GC_{Lie} and GC_{As} ``assembled fromA'A' graphs with some additional structures. The graph complex GC_{Com} (resp. GC_{Lie}, GC_{As}) is related to the operad Com (resp. Lie, As) governing commutative (resp. Lie, associative) algebras. Although these complexes (and their generalizations) are easy to define, it is hard to get very much information about their cohomology spaces. In my talk, I will describe the links between these graph complexes (and their modifications) to the cohomology of the moduli spaces of curves, the group of outer automorphisms of a free group, the absolute Galois group of rationals, finite type invariants of tangles, and the homotopy groups of embedding spaces.