Dissipative Henon maps are polynomial automorphisms of $C^2$ which can be viewed as perturbations of one-dimensional quadratic polynomials. We will overview several themes in this area that have been advanced in recent years (classification of periodic Fatou components, ``critical points" in the Fatou components, problem of existence of wandering domains, hedgehogs for Cremer maps, and bifurcations in holomorphic families of Henon maps).