In this talk we present some results about the internal dynamics of simply connected wandering domains of a transcendental entire map f. While the dynamics in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected, bounded wandering domains have so far eluded classification. We fill this gap by classifying their dynamics in terms of the hyperbolic distance between iterates and, at the same time, by whether orbits converge to the boundary of the sequence of domains and, by means of approximation theory, we show that all possibilities are realizable. Under appropriate assumptions, we can ensure that the resulting wandering domains are Jordan domains. This is joint work with A.M.Benini, V.Evdoridou, P.Rippon and G.Stallard