We consider simple extended dynamical systems with quenched disorder.
It is shown that these systems exhibit anomalous transport properties
such as the total suppression of chaotic diffusion and anomalous drift.
The relation to random walks in random environments, in particular to
the Sinai model, explains in addition the occurrence of ageing in such
dynamical systems. Anomalous transport is connected to spectral
properties of corresponding propagators and by escape rates in these
systems. New classes of anomalous transport behaviour with clear
deviations from the behaviour of Sinai type are found and discussed for
generalizations of these models.