  We discuss recent work on the static and dynamical properties of the
asymmetric exclusion process, generalized to include the effect of disorder. We
study in turn: random disorder in the properties of particles; disorder in the
spatial distribution of transition rates, both with a single easy direction and
with random reversals of the easy direction; dynamical disorder, where
particles move in a disordered landscape which itself evolves in time. In every
case, the system exhibits phase separation; in some cases, it is of an unusual
sort. The time-dependent properties of density fluctuations are in accord with
the kinematic wave criterion that the dynamical universality class is
unaffected by disorder if the kinematic wave velocity is nonzero.
