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abstract: Most of the baryonic matter in the Universe is permeated by magnetic fields, which affect many, if not most of astrophysical phenomena in diffuse gas. Recent years have been marked by a worldwide growing interest in the magnetic fields, their origin, and their influence on the formation and evolution of astrophysical objects (stars, galaxies, cooling flows). This interest is growing as it has become feasible to trace magnetic fields in molecular clouds, over vast extensions of the Milky Way and to study extragalactic magnetic fields, including fields in clusters of galaxies. With the combination of various techniques, including Zeeman and Faraday rotation measurements with polarimetry it is now possible to undertake quantitative studies of magnetic fields, the results of which can be compared with the results of dynamo and MHD turbulence simulations, subjects that have also made huge strides within several recent years.

The time is ripe to address many vital questions related to the origin of astrophysical magnetic fields in diffuse gas and quantify their effects on transport processes in the interstellar medium of spiral galaxies and in the intracluster medium, in order to get better insight into star formation, acceleration of cosmic rays, and transfer of matter and energy between the diffuse and dense gas. Thus it is really important to bring together world experts to identify the present state of art of the subject, summarize the progress achieved recently, as well as to outline the remaining outstanding problems, and review the progress of the 21st century instruments and projects for cosmic magnetic field investigation such as, upgraded SOFIA, PLANCK, LOFAR, ALMA and SKA.

This Joint Discussion at the IAU General Assembly will provide an excellent forum for this timely undertaking. Because of the cross-disciplinary nature of the subject and the intended discussion sessions, we expect to catch the attention and interest of a wide range of astrophysicists, including specialists in space and Solar physics. In fact, we plan to have also talks that would discuss magnetic fluctuations measured by spacecrafts.