  We state and prove four types of Lieb-Robinson bounds valid for many-body
open quantum systems with power law decaying interactions undergoing out of
equilibrium dynamics. We also provide an introductory and self-contained
discussion of the setting and tools necessary to prove these results. The
results found here apply to physical systems in which both long-ranged
interactions and dissipation are present, as commonly encountered in certain
quantum simulators, such as Rydberg systems or Coulomb crystals formed by ions.
