  Coupling a quantum many-body system to an external environment dramatically
changes its dynamics and offers novel possibilities not found in closed
systems. Of special interest are the properties of the steady state of such
open quantum many-body systems, as well as the relaxation dynamics towards the
steady state. However, new computational tools are required to simulate open
quantum many-body systems, as methods developed for closed systems cannot be
readily applied. We review several approaches to simulate open many-body
systems and point out the advances made in recent years towards the simulation
of large system sizes.
