The discovery of dark halos, spectroscopic evidence that elliptical galaxies are dominated by collisionless dynamics and the opening of new observational windows (especially in the near-infrared) able to provide direct information on the underlying mass distribution in spiral galaxies, have significantly changed our perception of the internal structure of galaxies. The modelling tools and the theories developed to explain many interesting observations (from the study of global spiral and bar modes of galaxy disks to the construction of self-consistent anisotropic collisionless models to explain the universality of the luminosity profile of elliptical galaxies) present many analogies with parallel work in the physics of electromagnetic plasmas. Beyond specific mechanisms, the main source of similarities between the two fields is probably to be found in the common semi-empirical approach, where the major struggle is to set up the most appropriate equations to describe inherently complex systems, governed by collective behaviour in the presence of long-range forces. At the frontier of current research in extragalactic astrophysics, the Hubble space telescope and new large telescopes from the ground are giving us a view of the early dynamical stages of galaxies and on the small scale for relatively nearby galaxies, unprecedented accurate data on their structure and kinematics. After focusing on some recent results relative to the collective dynamics of stellar systems, we will identify a few basic questions that remain unresolved, where the study of galaxies as gravitational plasmas may help significantly towards further progress.
On the origin of cosmological magnetic fields by plasma instabilities