Turbulence in space plasmas and beyond

Most of the visible matter in the Universe is in the form of highly turbulent plasmas. For a long time the turbulent character of astrophysical fluids has been neglected and not well understood. One reason for this is the extremely complicated physics involved in astrophysical processes ranging from the machinery of stars, solar and stellar winds, accretion disks to interstellar clouds and galaxies. The other reason is that turbulence constitutes in itself a difficult subject where most of the fundamental results belongs to the incompressible hydrodynamics. Nevertheless, significant theoretical progress has been made during the last years to incorporate some ingredients like compressibility or small-scale plasma physics which are fundamental in astrophysics. This paper reviews some of these results with a strong focus on space plasmas (solar wind, solar corona). Turbulence in interstellar clouds (supersonic flows) and cosmology (space-time fluctuations) are also briefly mentioned.