Transcendendental Henon maps are automorphisms of $C^2$ with constant Jacobian, of the form $F(z,w)=(f(z)+\delta w,z)$, with $f$ entire transcendental and $\delta$ complex number. They are a natural transcendental analogue of the popular class of polynomial Henon maps. Thanks to their special form, and the advanced knowledge of the dynamics of one dimensional maps, and despite many open questions, transcendental Henon maps form a class of nonpolynomial automorphisms of C^2 for which it is actually possible to prove general theorems, yet exhibit a variegated dynamical behaviour with many new features with respect to their polynomial counterpart. We will look at both the stable and the chaotic dynamics of such maps. This is joint work with Leandro Arosio, John Erik Fornaess and Han Peters.