This is an introductory text reviewing Lieb-Robinson bounds for open and
closed quantum many-body systems. We introduce the Heisenberg picture for
time-dependent local Liouvillians and state a Lieb-Robinson bound that gives
rise to a maximum speed of propagation of correlations in many body systems of
locally interacting spins and fermions. Finally, we discuss a number of
important consequences concerning the simulation of time evolution and
properties of ground states and stationary states.Comment: 13 pages, 2 figures; book chapte
