  Magnetic fields of cosmic bodies are generated by the hydromagnetic dynamo
effect in moving electrically conducting fluids, such as liquid metals or
plasmas. Once produced, cosmic magnetic fields are able to act back on moving
fluids. This back-reaction may have dramatic consequences for cosmic structure
formation, with the magnetorotational instability (MRI) in accretions disks as
the most prominent example. Considerable theoretical and computational progress
has been made in understanding both the dynamo effect as well as magnetically
triggered flow instabilities. Complementary to this, the last fifteen years
have seen much effort in studying both effects in liquid metal experiments. We
summarize the history of these experiments, discuss their main results and
their limitations, and give an outlook on future activities.
