A renormalization operator will be introduced to study Henon maps. The geometry of the Cantor attractor of an infinitely renormalizable Henon map and the global topological properties of such maps will be discussed. There are universal properties. However, the average Jacobian controls two-dimensional phenomena responsable for non-rigidity. Finally, it is shown that hyperbolicity is dense in the zero entropy part of a neighborhood of any infinitely renormalizable map. Moreover, there are countable many hyperbolic components accumulating at such a map.