Let U be a Fatou component of a transcendental entire function. If U is not eventually periodic then it is called a wandering domain. Although Sullivan's celebrated result showed that rational maps have no wandering domains, transcendental entire functions can have wandering domains. In this talk we will look at internal dynamics of simply connected wandering domains and we will give a nine-way classification of these domains. We will also show that all nine types of wandering domains that arise from this classification are realizable. This is joint work with Anna Miriam Benini, Nuria Fagella, Phil Rippon and Gwyneth Stallard.