A transcendental Henon map is a biholomorphic map of $mathbb C^2$ of the form $F(z,w)=(f(z)+aw, z)$ with $f(z)$ an entire transcendental function in one variable. We go over basic properties of the Fatou set for such maps and construct examples of transcendental Henon map with Baker domains, with wandering domains whose orbits converge to infinity, and with oscillating wandering domains.