  We discuss how the nine-way classification scheme devised by Benini et al.
for the dynamics of simply connected wandering domains of entire functions,
based on the long-term behaviour of the hyperbolic distance between iterates of
pairs of points and also the distance between orbits and the domains'
boundaries, carries over to the general case of multiply connected wandering
domains of meromorphic functions. Most strikingly, we see that not all pairs of
points in such a wandering domain behave in the same way relative to the
hyperbolic distance, and that the connectivity of the wandering domain greatly
influences its possible internal dynamics. After illustrating our results with
the well-studied case of Baker wandering domains, we further illustrate the
diversity of multiply connected wandering domains in general by constructing a
meromorphic function with a wandering domain without eventual connectivity.
Finally, we show that an analogue of the "convergence to the boundary"
classification of Benini et al. does hold in general, and add new information
about how this convergence takes place.
