Phase separation in disordered exclusion models

The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically i nduce phase separation in a range of densities. In the particlewise case th e existence of stationary product measures in the homogeneous phase implies that the critical density can be computed exactly, white for sitewise diso rder only bounds are available. The coarsening of phase-separated domains s tarting from a homogeneous initial condition is addressed using scaling arg uments and extremal statistics considerations. Some of these results have b een obtained previously in the context of directed polymers subject to colu mnar disorder.